125PhysicsProjects

fortheEvilGenius

2

EvilGeniusSeries

Bike,Scooter,andChopperProjectsfortheEvilGenius

BionicsfortheEvilGenius:25Build-It-YourselfProjects

ElectronicCircuitsfortheEvilGenius:57LessonswithProjects

ElectronicGadgetsfortheEvilGenius:28Build-It-YourselfProjects

ElectronicGamesfortheEvilGenius

ElectronicSensorsfortheEvilGenius:54ElectrifyingProjects

50AwesomeAutoProjectsfortheEvilGenius

50GreenProjectsfortheEvilGenius

50ModelRocketProjectsfortheEvilGenius

51High-TechPracticalJokesfortheEvilGenius

FuelCellProjectsfortheEvilGenius

MechatronicsfortheEvilGenius:25Build-It-YourselfProjects

MOREElectronicGadgetsfortheEvilGenius:40NEWBuild-It-YourselfProjects

101OuterSpaceProjectsfortheEvilGenius

101SpyGadgetsfortheEvilGenius

123PIC®MicrocontrollerExperimentsfortheEvilGenius

123RoboticsExperimentsfortheEvilGenius

PCModsfortheEvilGenius

ProgrammingVideoGamesfortheEvilGenius

SolarEnergyProjectsfortheEvilGenius

TelephoneProjectsfortheEvilGenius

22RadioandReceiverProjectsfortheEvilGenius

25HomeAutomationProjectsfortheEvilGenius

3

125Physics

Projectsforthe

EvilGenius

JERRYSILVER

4

Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States

CopyrightActof1976,nopartofthispublicationmaybereproducedordistributedinanyformorbyanymeans,orstoredin

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5

AbouttheAuthor

JerrySilver has developed components for terrestrial photovoltaic systems and designed solar arrays currently providing

power for more than 20 commercial and NASA satellites. He participated in the production of high-performance

semiconductormaterialsusedforcellphonetransistors,opticalcommunication,andmultijunctionsolarcells.Mr.Silverholds

aB.S.inEngineeringPhysicsfromCornellUniversityandanM.S.inPhysicsfromtheUniversityofMassachusetts.Mr.Silver

currentlyteachesintheNewJerseyarea.

6

ThisbookisformywifeJoanieandmykidsAllyandDanny.

7

Acknowledgments

The author would like to gratefully acknowledge SteveGrabowski, Dan Silver, Danielle Buggé, Tracey Jameson, MichaelDershowitz,theWallshes,BrookhavenLabs,JohnKenney,andthefolksatPASCOforassistancewiththeillustrationsinthis

book.Inaddition,specialthanksareofferedtoSteveGrabowski,ChisAleo,TiberiuDragoiu,RobinNolte,TomMisniak,and

KimFeltreforenablingmetobepartofaworldwherephysicsisappreciated,promoted,andsharedonadailybasis.

8

Contents

Introduction

Section1Motion

Project1Gettingstarted.Constantvelocity.Runningthegauntlet.

Project2Picturingmotion.Gettingamoveon.

Project3Thetortoiseandthehare.Playingcatch-up.

Project4Howdoesasailboatsailagainstthewind?Componentsofforce.

Project5Steppingonthegas.

Project6Rollingdownhill.Measuringacceleration.

Project7Independenceofhorizontalandverticalmotion.Basketballtossedfromarollingchair.

Project8Targetpractice.Horizontalprojectile—rollingoffatable.

Project9Takingaim.Shootingaprojectileatatarget.

Project10Mondaynightfootball.Trackingthetrajectory.

Project11Monkeyandcoconut.

Section2GoingAroundinCircles

Project12Whatisthedirectionofasatellite’svelocity?

Project13Centripetalforce.Whatisthestringthatkeepstheplanetsinorbit?

Project14Agravitywell.Followingacurvedpathinspace.

Project15Howfastcanyougoaroundacurve?Centripetalforceandfriction.

Project16Ping-pongballsracinginabeaker.Centripetalforce.

Project17Swingingapailofwateroveryourhead.

Section3Gravity

Project18Featherandcoin.

Project19Howfastdothingsfall?

Project20Thebuckstopshere(thefallingdollar).Usingametersticktomeasuretime.

Project21Weightlesswater.Losingweightinanelevator.

Project22Whatplanetareweon?Usingaswingingobjecttodeterminethegravitationalacceleration.

Section4ForceandNewton’sLaw

Project23Newton’sfirstlaw.WhattodoifyouspillgravyonthetableclothatThanksgivingdinner.

Project24Newton’sfirstlaw.Pokerchips,weightonastring,andafrictionlesspuck.

Project25Newton’ssecondlaw.Forcinganobjecttoaccelerate.

Project26Newton’sthirdlaw.Equalandoppositereactions.

Project27Newton’sthirdlaw.Bottlerockets.Whydotheyneedwater?(SirIsaacNewtoninthepassenger’sseat.)

Project28Pushingwater.Birdsflyinginsideatruck.

Project29Slippingandsliding.

Project30Springs.Pullingback.Thefurtheryougo,theharderitgets.

Project31Atwood’smachine.Averticaltugofwar.

Project32Terminalvelocity.Fallingslowly.

Project33Balancingact.Painteronascaffold.

Project34Hangingsign.

Project35Pressure.Implodingcans.

Project36Pressure.Supportingwaterinacup.

Project37Pressure.Sometimesthenewscanbeprettyheavy.

Project38Archimedes’sprinciple.Whatfloatsyourboat?

Project39Cartesiandiver.

Project40Anair-pressurefountain.

9

Project41Blowingupamarshmallow.Lessiss’more.Whyastronautsdonotuseshavingcreaminspace.

Project42Relaxingonabedofnails.

Project43Blowinghangingcansapart.WhatBernoullihadtosayaboutthis.

Project44Centerofmass.Howtobalanceabroom.

Project45Asimplechallenge.Moveyourfingerstothecenterofameterstick.

Project46Centerofgravity.Howfarcanastackofbooksextendbeyondtheedgeofatable?

Project47Centerofmass.Theleaningtowerofpizza.

Section5Energy/Momentum

Project48Thependulumandyourphysicsteacher’sMingdynastyvase.

Project49Twoslopes.Differentangle,sameheight.

Project50Racingballs.Thehighroadversusthelowroad.Whichwins?

Project51Linearmomentum.Wherecanyoufindaperfect90-degreeangleinnature?

Project52Elasticcollisions.

Project53Inelasticcollision.Stickingtogether.

Project54Impulseandmomentum.Eggstremephysics.

Project55Usinggravitytomoveacar.

Project56HowcanCSImeasuremuzzlevelocity?Theballisticpendulum.

Project57Angularmomentum.Ridingabike.

Project58Momentofinertia.Iceskatersanddumbbells.

Project59WhatcausedVoyagertopointinthewrongdirection?

Project60Momentofinertia.Thegreatsoupcanraceorthat’showIroll.

Project61Makingwaves.IthoughtInodethis.

Project62Rollinguphill.

Project63Gettingaroundtheloop.Fromhowfarabovethegrounddoestherollercoasterneedtostart?

Section6SoundandWaves

Project64Whatdoessoundlooklike?Oscilloscopewaveforms.

Project65Rippletank.

Project66Simpleharmonicmotion.Theswingingpendulum.

Project67Simpleharmonicmotion.Thespringpendulum.

Project68Generatingsinewaves.

Project69Naturalfrequency.

Project70Bunsenburnerpipeorgan.Resonantfrequency.

Project71Springsandelectromagnets.Resonance.

Project72Speedofsound.Timinganechooldschool.WhyGalileocouldn’tdothiswithlight.

Project73Speedofsound.Resonanceinacylinder.

Project74Racingagainstsound.Dopplereffect.

Project75Addingsounds.Beatfrequency.

Project76Pendulumwaves.

Project77Usingwavestomeasurethespeedofsound.

Section7Light

Project78Rayoptics.Tracingthepathoflightusingalaser.

Project79Twocandles,oneflame.

Project80Laserobstaclecourse.

Project81Lightintensity.Puttingdistancebetweenyourselfandasourceoflight.

Project82Howdoweknowthatlightisawave?ThomasYoung’sdoubleslitexperimentwithadiffractiongrating.

Project83Howtomeasurethesizeofalightwave.

Project84Thespeedoflightinyourkitchen.Visitingthelocalhotspots.

Project85Refraction.Howfastdoeslighttravelinairorwater?

Project86Polarization.Sunglassesandcalculatordisplays.

10

Project87Whatisthewireofafiber-opticnetwork?Totalinternalreflectionusingalaserandatankofwater.

Project88Thedisappearingbeaker.

Section8HotandCold

Project89HowmuchheatisneededtomeltGreenland?Heatoffusion.

Project90Awaterthermometer.

Project91Whatisthecoldestpossibletemperature?Estimatingabsolutezero.

Project92Liquidnitrogen.

Project93Boilingwaterinapapercup.

Project94Boilingwaterwithice.

Project95Seebeckeffect/Peltiereffect.Semiconductorheating.

Section9ElectricityandMagnetism

Project96Staticcharges.

Project97Makinglightning.ThevandeGraaffgenerator.

Project98TheWimshurstmachine.Separatingandstoringcharges.

Project99Runningintoresistance.Ohm’slaw.

Project100Circuits:Bulbsandbuzzers.

Project101Howdoesheataffectresistance?

Project102Resistivity.Canironconductelectricitybetterthancopper?

Project103Storingcharge.Capacitors.

Project104Isthemagneticforcemorepowerfulthangravity?

Project105Magneticlevitationusinginduction.Electromagneticringtosser.

Project106Magneticlevitationusingsuperconductivity.TheMeissnereffect.

Project107Movingelectronsproduceamagneticfield.Oersted’sexperiment.Themagneticfieldofacurrent-carryingwire.

Project108Faraday’sexperiment.Currentgeneratedbyamagnet.

Project109Ifcopperisnotmagnetic,howcanitaffectafallingmagnet?Lenz’slaw.

Project110Effectofamagnetonanelectronbeam.Theright-handruleformagneticforce.

Project111Whatistheshapeofamagneticfield?

Project112Whathappenstoacurrent-carryingwireinamagneticfield?

Project113Ano-frillsmotor.

Project114Magneticaccelerator.

Project115Alternatingcurrent.

Project116Thediode.Anelectronicone-wayvalve.

Section10TheEarth

Project117MeasuringtheEarth’smagneticfield.

Project118WeighingtheEarth.

Section11TheTwentiethCentury

Project119Whatisthesizeofaphoton?

Project120HowisahydrogenatomliketheNewJerseyTurnpike?SeeingtheenergylevelsoftheBohratom.

Project121Photoelectriceffect.

Project122Millikanoil-dropexperiment.Mysterymarbles.Understandinghowtheexperimentworked.

Project123Ping-pongballchainreaction.

Project124Thesodiumdoublet.Whydowethinktheelectronhasbothupanddownspins?

Project125Buildingacloudchamber.Whymuonsshouldnotbehere.Specialrelativity.

AppendixA

AppendixB

Index

11

Introduction

WhoThisBookIsWrittenFor

Thisbookhasbeenwrittenforanyonewhoisinterestedin,obsessedwith,orsimplymildlycuriousaboutexploringphysics.

Theexperiments in thisbookare intended toserveasa resource for teachersatall levels touse inplanning laboratory

activitiesfortheirclassesandtogetideasfordemonstrations.Thisbookcanalsoprovideawayforanyonenotnecessarily

directly involvedwith an academic physics class—including parents, scout leaders, and hobbyists—to pursue theworld of

physicsasfarastheirintereststakethem.Youngchildren—andthosefacilitatingtheireducation—willbeabletoappreciate

manyoftheseexperimentsonanintuitivelevel—perhapsonedaytorevisitthemingreaterdepth.

Ifyouarelookingforscienceproject ideas,youshouldbeabletofindsomethinginthesepagestoworkwith.Students

involvedinafirst-yearhighschoolorcollegephysicsclasswillfindtheoverallsequencefamiliarandhopefullywon’thave

toomuchtroublefindingtheirwayaround.

Iimaginethatreaderswithawiderangeofinterests,backgrounds,andavailableresourceswilllookthroughthesepages

forideasaboutphysicsexperiments.Forthisreason,Ihavewrittentheprojects/experimentstobeaccessibletoreadersina

numberofdifferentwaysandonavarietyoflevels.Mostoftheexperimentsincludeawaytogetstartedwithoutrequiring

elaborateequipment.

HowThisBookIsOrganized

Eachsectionstartswithalistofrequireditemsfollowedbystep-by-stepmethods.Becausethereisoftenmorethanoneway

to do a project, various options are given to accommodate varying experience, available resources, and interest levels

amongreaders.

Theexpectedoutcomefortheexperimentsisgiventohelpyouinterpretyourexperimentalresults.Firstyouwillfindthe

mostqualitativeandintuitiveinsights,followedbyincreasinglydetaileddescriptions.Forthosewhoareinterested(andonly

thosewhoareinterested)equationsareprovidedtocompletetheexplanationforwhytheexperimentswork.Thereaderis

invitedtopursueonlyasmuchoraslittledetailastheycareto.Thisbookisnotintendedtobeatextbookonphysicstheory.

Ihavetried,however,tohelpreadersconnectwiththenextsteptheymightbereadytotake.Justtobesure,eachproject

hasaconclusionthatspellsoutthepointoftheexperiment.

TheWorldofPhysics:DiscoveryandRediscovery

On more than one occasion in the history of physics, the greatest advances have taken place at a time when the

conventionalwisdomofthedaywasthateverythinghadalreadybeendiscoveredandallthatwaslefttoworkoutwerethe

details.Thehands-onapproachpresentedhere is tohelp the reader to (re-)discoverphysicsdirectly. (All Iask, is in your

acceptancespeechfortheNobelPrizeforphysics,youreserveafewkindwordsforthisbook.)

Thereistypicallymorethanonewaytodomanyoftheseexperiments.Atleastoneprocedurefromstarttofinishisgiven

foreachexperiment.Butalsoarangeofalternativeapproachesandextensionscanbefoundformostofthem.Hopefully

thisbookwillleaveyouwithideas,notonlyforhowtodotheseexperiments,butalsoforhowtocomeupwithexperimental

ideasofyourown.

WhatYouWillNeed:ToolBin/PartsList

TheBasics

Eachoftheprojectsinthisbookhasaspecificpartslist,called“Whatyouneed.”Becausedifferentreaderswillhaveaccess

12

todifferenttypesofequipment,alternativeapproachesarepresented.AlistofmajorsuppliersisgiveninAppendixAatthe

endofthisbook.

Thefollowingaresomeoftheitemsyoumaywanttohavehandy.Mostoftheseitemsareavailableintypicalphysicslabs

andmanycanbeimprovised.

stopwatch—aone-tenth-secondresolutionissufficientbecauseiteasilyexceedshumanreactiontime.

ring stands—many of the projects in this book involve supporting or holding other components of the apparatus.

Whilethiscanbeaccomplishedinotherways,havingabasicsetofringstandswithafewclampsgivesyoumore

timetofocusonsettinguptheexperiment.

meterstick—most metersticks have millimeter markings. Metersticks often serve multiple functions in addition to

measuring,suchasholdinglensesandmirrors.Thethinneronesusuallyfitbetterwiththesupportsusedinoptical

experiments.

tapemeasure—mostofyourworkwillbeinmeters.Itiseasyenoughtoconvertfeettometers,butgiventhechoice,

atapemeasurewithmetricdivisionsispreferable.

ruler—withmillimeterdivisions.

spring(s)—springswithvaryingdegreesofstiffnesstocompareareuseful.Thebestareonesthatcanbepartially

stretchedbyareasonableweight.

pulley—thelessfrictionandthelowestmass,thebetter.

stringandrope—variouskinds.Youwillwantatleastsomethinstrongstring.Weakerstringthatcanbreakplaysa

roleinProject24.

massset—arangeofmassesfrom10gto1kg(1000g).Theyshouldhaveanattachmentpointfromthetopand,

ideally,alsofromthebottom.

springscale—thesecomeinvariousranges,fromafullscalereadingof2.5newtons(255g)toafull-scalereading

of50newtons(5100g). Ifyouaredoingdemonstrationsbeforeagroup,alargecircularversionofthescalewith

oversize lettering is theway to go. (Not to quibble, butweight is a force that is read in newtonsandmass is a

measure of an object’s inertia, which is measured in grams. Physics purists definitely prefer weighing objects in

newtons.)MostofourworkwillbeintheSystemInternational(SI),which,tooversimplify,isafancynewnameforthe

metricsystem.Springscalesalsocomecalibrated inpounds (and if youmust, dynes,whichalmostnooneuses

today)—ifyouhappentohaveone,youcandothemath.ConversionfactorscanbefoundinAppenidixB.

balance—low-endelectronicbalanceshavebecomemuchmoreaffordableandcanbepurchasedforlessthan$50.

Otheroptionsincludeanalogtriple-beamscalesorthemoreelaboratedigitalbalances.

wire—severalmetersofinsulatedwire,suchasAmericanwiregauge(AWG)18,20,or22.

jumperwires—jumperwireswithvariouscombinationsofattachmentsmaketheelectricalprojectsgoalotsmoother.

Onetermination iscalledabananaplug,whicheasilyconnectsacircuit toameterorapowersupply.Another is

springloadedandgripsontoanelectricalconnectioncalledanalligatorclip.(IntheUK,somepeoplerefertothese

“croc”clips.Iamnotmakingthisup.)

DCpowersupply (orbatterieswithawireconnection)—someprojects require thecapability toadjust thevoltage.

Thisrequiresanadjustablepowersupply,whichcanbepurchasedasacomponent.Thepowersupplypictured in

FigureI-1(PASCO,partnumberSE-8828)costslessthan$150,andenablesyoutodoalltheprojectsinthisbook

thatcallforaDCpowersupply.ReasonablypricedDCpowersuppliescanalsobepurchasedfromSargent-Welch,

partnumberWLS-30972-81orFlinn,partnumberAP5375.

Somelabsalsohaveadjustablepowersuppliesbuiltintothelabbenches.IfyourDCpowersupplyconsistsofabattery,

thevoltagecanbemadevariablebyusingvariouscombinationsofresistors.Otheroptionsforapowersupplyincludea

hand-heldgenerator thatproducesaDCvoltagewhenacrank ismanually turned (suchasPASCO,partnumberEM-

13

8090orSE-8645,orSargent-Welch,partnumberWL2420).

FigureI-1Powersupply.CourtesyPASCO.

batteries—CorD cell battery and holder. Youwill not needa battery if you haveaDCpower supply except for

Project113.

electrical meters—the most useful and versatile meter is a multimeter. Multimeters perform the functions of

ammeters, voltmeters, ohmmeters, and many can also be used as a digital thermometer. Multimeters can be

acquiredforlessthan$50,whichinmanycasesislessexpensivethanstand-aloneammetersorvoltmeters.Some

projectsrequirebothanammeterandavoltmeter,soforthoseprojects,twomultimetersareneeded.Ifamultimeter

is not available, a separate ammeter and voltmeter are needed. Figure I-2 shows a multimeter available from

Sargent-Welch, part numberWLS-30712-60 (also fromPASCO, part numberSE9786A, or Frey, part number 15-

531978-21)thatworkswithalltheprojectsinthisbook.Onewordofcaution:themultimeterismuchmoreversatile

thanadedicatedammeterorvoltmeterformostpurposes.However,ifusedincorrectly,suchasbybeingplacedin

serieswithtoohighacurrent,youcaneitherblowafuse,orworse,damagethemeter.

14

FigureI-2Multimeter.CourtesyPASCO.

galvanometer—agalvanometerisaverysensitiveammeterthatdisplayssmallelectricalcurrents.

electroscope—thisisasimpledevicethatmeasuresthepresenceofstaticelectriccharges.Theyareinexpensive

andavailablecommercially.Homemadeversionsconsistofasmallballattachedbyawire.Thewireisconnectedto

twometalfoilleaves,whichareprotectedfromdischargeandaircurrentsbyaglassenclosure.

magnets—barandhorseshoemagnets

glassware—beakers,flasks

rubberstoppers—two-holeandno-holerubberstopperstofitflasks

hotplate—preferablyadjustablewithaceramictop

alcoholthermometer—mercurythermometersareno-no’sinmostlabstodaybecauseoftheenvironmentalproblems

creatediftheybreak.

hydrogentubewithhigh-voltagepowersupply

calculator—veryoftenthe ideasandkey insights inphysicsarerevealedanddiscoveredbydoingacalculation.A

simplescientificcalculator,suchasaTI-30orequivalent,canbehelpfulinmanyoftheprojectsinthisbook.

Computersareusedinmanyways,including:

–Collectingdatafrommotionsensorsandothermeasurementdevices(suchaslight,sound,force,current,andvoltage

sensor).

–Analyzingdatainaspreadsheet,suchasExcel,toidentifymathematicalmodels.

–Soundcardoscilloscope(seeProject64).

laserpointer—alaserpointerwithareplaceable(or,betteryet,rechargeable)AAbatteryisthemostversatileinthe

longrun.Thesimplelaserpointeravailableinmanydollarstoresworkswell,butislessreliable.

lenses—convex,concave,semicircular,rectangular,45-degree,60-degree,andright-angleprisms.Somelensesare

“smoky,”consistingofscatteringparticulatesintheglassthatmakethelightbeamsvisibleinthelens.Otherlenses

have a magnetic backing that makes them convenient to mount on a magnetic chalkboard or whiteboard. This

makesiteasytoenableraytracingonachalkboard.Itispossibletoglueastrongmagnettoalens,sotheycanbe

mountedonachalkboard.

mirrors—flat,concave,convex

tape—ducttape,maskingtape,electricaltape.Oneoften-overlookedprincipleofphysicsisthereisnosuchthingas

havingtoomuchtape.

Thingsthatarenicetohave

15

motionsensor—forlessthanthecostofavideogameconsole,youcangetamotionsensorthatconnectswithyour

computor.Motionsensors(suchasPASCO,partnumberPS-2103A)enablemeasurementofanobject’spositionfor

varioustimes.FigureI-3showsthemotionsensor.TheDataStudiosoftwarethatcomes(free)withPASCOmotion

sensors letsyougenerategraphsofdistanceversustime,velocityversustime,andaccelerationversustimewith

little prior experience with this equipment. The motion sensor requires a simple interface to the computer. The

simplestoftheseapproachesconnectstothecomputer’sUSBport(PS-2100A)andrequiresnoadditionalelectrical

power.ThreesensorscanbeconnectedtoacomputerusingthePS-2001.

FigureI-3Motionsensor.CourtesyPASCO.

Ahand-helddataloggersuchasPASCO’sXplorerGLX(partnumberPS-2002)functionsinasimilarwaywithvarious

sensors eliminating the need for a computer. This also enables measurements to be taken at more remote

locations.

oscilloscope—wave formsgenerated by soundpicked up by amicrophoneor electrical signals can be displayed

graphicallyonanoscilloscope. Ifyouhaveone,youcandoanumberof interestingthingswithascope.Because

eachoscilloscopeissomewhatdifferent,youalsoneedagoodmanualorapatientfriendtogetyoustarted.Ifyou

do not have a physical oscilloscope, you can inexpensively acquire software that can enable the sound card

commonlyavailableincomputerstoserveasasurprisinglyfunctionaloscilloscope.Detailsonhowtodothiscanbe

foundinProject64.

dry ice—the cloud chamber described in Project 125 uses dry ice, which can be obtained from welding supply

companies,scientificlabs,orchemicalspecialtycompanies.Ifyouareabletogetdryice,youmaywanttogeta

littleextratoexploreotherlow-temperaturephysicsexperiments.Becausedryice,whichisactuallysolidifiedcarbon

dioxide,issocold,youshouldtakeprecautionstoavoidprolongedcontactwiththebody.Useeyeprotectionwhen

workingwithdryice,especiallyifyouarebreakingitintosmallerpieces.

HoverPuck—somephysicslabsuseairtrackstoeliminatefriction.Alower-costoptionistouseaHoverPuckthat

floatsinanearlyfrictionlessmanneracrossthefloor.Thisiscalledoutasanoptioninafewoftheexperimentsin

thisbook.HoverPucksareavailablefromPASCO,partnumberSE-73358,andKick ItStick ItDiscfromSargent-

Welch,partnumberWLS-1764-09.

liquid nitrogen—liquid nitrogen is needed tomake the ceramicmaterial described in Project 106 cold enough to

becomesuperconducting.Aswithdryice,liquidnitrogenisamaterialthatisinterestinginitownrightandisexplored

inProject92.Itmaymakesensetoplanbothactivitiestogether.Justsoyouknow:dryicedoesnotgetcoldenough

todoProject106andliquidnitrogenisnotrecommendedforProject125becauseitistoocold.Liquidnitrogenmust

bestoredinaspeciallydesignedthermalcontainercalledaliquidnitrogendewar,whichsafelyhandlesthepressure

thatbuildsastheliquidnitrogenwarmsup.Aregularthermosbottlewithasealedcaporanyothertypeofsealed

containershouldnotbeused.Liquidnitrogenisdistributedinspeciallydesignedstoragecylinderstoorganizations

16

thatdo low-temperaturestudies, thermalcycling to testproduct reliability,andthatuse largevolumesofgaseous

nitrogen.

vacuumpump—avacuumpumpisusedinProjects18,41,and94.

Wish-list

Not so many years ago, some of the greatest physics experiments remained the province of obscure physics labs in

exclusiveuniversities.Today,theseexperimentsarewithinthereachofmanyphysicsdepartmentswithamoderatebudget.

Becausethepricetagfordoingtheseexperiments isthousands,ratherthanhundreds,ofdollars,formostofus,theyare

consideredheretobewish-listexperiments.Foreachofthese,asimpler,low-budgetoptionispresented.Thethreewish-list

experimentsreferredtointhisbookare:

Millikanoil-dropexperiment(PASCO,partnumberAP-8210,andFlinnScientific,partnumberAP5671)

photoelectriceffectapparatus,suchastheDaedelonEP-05(availablefromwww.daedelon.comorFlinnScientific,

partnumberAP5768).

Cavendishgravitationalconstant(PASCO,partnumberAP-8215)

Yardsalephysics

At the other end of the funding spectrum are items that can be adapted for use in physics experiments. As has been

demonstratedbymanyofthegreatscientistsofthepast,muchcanbeaccomplishedthroughresourcefulnessandingenuity.

Besidesthebargainhuntersandantiquedealers,physicsenthusiastscan,onoccasion,beobservedlookingforunnoticed

treasureatyardsaleswhereotherpeoplefailtoseethetruevalue.Herearesomeoftheitemsyoumightwanttoaddto

yourbagoftricks.

bowling ball—a bowling ball makes a good pendulum mass that can also give one of the most accurate

measurementsofgravitationalacceleration.AbowlingballcanbeusedinProjects19,22,26,or66, ifavailable.A

heavy-dutyscreweyecanbeanchoredbytapingintoapilotholesmallerthanthediameterofthescrew.Becareful

and thoroughly test your mechanical connection before experimenting. Bowling balls can also come in handy in

investigatingcollisions.

swivelchair—youwantonethatrotateswithaslittlefrictionaspossible.Thisisusefulintheconservationofangular

momentumstudies.Justthebottompartwithouttheseatcanbeusedforstudyingspinningobjects.

bathroomscale—thiscanbeusedtoexplorestaticequilibriumandtorque.

blowdryers—ablowdryerisahandywaytoproduceareasonablysteadyairflow.ThisisusedtoexploreBernoulli’s

principleinProject43.

fishtanks—theoneswithglassbottomsareespeciallyusefulforopticalprojectsusinglaserbeams.Afishtankcan

bemade into a cloud chamber in Project125 or used as the container of amousetrap-fission demonstration in

Project123.

slideprojectors—oldslideprojectorsormovingprojectscanbegoodsourcesoflight.

laser levels—thesecanbeusedlikea laserpointer.Thebeamsareangledtoproduceavisible linealongawall,

whichcanbeadvantageousforraytracing.Theoutputmaynotbethebest-focusedpointsourceoflight,sothisis

notthebestchoice,forinstance,tousewithadiffractiongrating.

turntables—turntablescanbeadaptedforrotationexperiments.(Thiscanalsobeusefulforthedigitalgenerationto

seewhatahistoricdevicelikethephonographlookedlike.)

airhockeygames—theseworkwellwithCDsaspucksandcanbeagoodwaytoinvestigateelasticcollisions.

skateboards,rollerblades—todemonstrateNewton’sthirdlaw.

leafblower—ifyouhavea leafblower,youhavemostofwhatyouneedtoput togetheraone-personhovercraft.

With just the right-shaped opening these can be used to levitate a beach ball in a demonstration of Bernoulli’s

principle(Project43).

bicycletires—thesemakegoodgyroscopesandcanbeusedforangularmomentumexperimentssuchasinProject

57.

17

Christmas tree lights—thesearean inexpensiveandeasyway to studyelectrical circuits suchas inProject100.

Theyusuallycomeinstrandsofseriesandparallelcombinations.

Youneverknowwhatelsemightcome inhandy,suchasbuckets, rope,wire,hotplates,clamps, lazysusans,golfballs,

varioustools,andmotors.Keepyoureyesopen.

18

Section1

Motion

Project1

Gettingstarted.Constantvelocity.Runningthegauntlet.

TheIdea

Withlittleornofrictiontostopit,amovingobjectwillkeepmovingataconstantvelocity.Thisexperimentexploresafew

simplewaysyoucantakefrictionoutofthepicture.

WhatYouNeed

HoverPuck

tapemeasure

5stopwatches

maskingtape

severalpeopletoserveastimers

Method

1. Setupacourse that ishorizontalandfreeofobstructions.Doa trial run tomakesure theHoverPuckdoesnot

moveunlessit’spushedandthatitfollowsareasonablystraightline.(Ifyoudon’thaveaHoverPuck,abasketballor

othersimilarobjectwilldo.)

2. Placedistancemarkers,suchasmaskingtapelabels,atregularintervals.(Typicallyinphysics,metersareusedfor

distance.However,forthisprojectanyconvenientunitcanworkaslongasyou’reconsistentthroughout.)

3. Eachofthetimersshouldbeassignedtomeasurethetimeataspecificdistancealongthepath.

4. Timersshouldsettheirstopwatchestoreadzeroandbepreparedtostartmeasuringthetimeassoonastheobject

startsmoving.

5. Pushthepuck(orbasketball)inthedesignateddirection.Startwithamediumpush.SeeFigure1-1.

6. Asthepuck(orbasketball)passeseachmark,eachtimershouldstopthestopwatchandnotethetime.

7. Repeatwithaslowpush.Aslowpushisdefinedasslowerthanthemediumpush,butfastenoughnottobepulled

offcourseorstoppedbyfriction.

8. Repeatwithamediumpush.

19

Figure1-1NearlyfrictionlessmotioncanbeachievedusingaHoverPuck.

9. Repeatwithafastpush.Thismaybethemostchallengingonetotime,especiallyforthefirstcoupleoftimers.

10. Thevelocityforeachoftherunnerswillbetheslopeofthegraphwheredistanceisonthey-axisandtimeisonthe

x-axis.

AlternateApproach

Runners

1. Placethepeoplewiththetimersonthe10,20,30,40,and50yardlinesofafootballfield.

2. Usearunnerorseveralrunnerstorunfromthegoallinetothe50yardline.

3. Asinnumber2,getthetimethateachrunnerpassesthedesignateddistancemarker,andthenplotandinterpret

theresults.

ExpectedResults

Withconstantvelocity,eachofthegraphsshouldbelinear(astraightline).Thefastestrunnerhasthehighestslope,followed

bythemediumrunner,withtheslowestrunnerbringinguptherear.

If,forsomereason,themotionwasnotperfectlyconstant,thepointsthatdifferedwillnotbeontheline.Forinstance,if

20

theassumptionthatfrictioncanbeignoredisnotcompletelyvalid,youmayseesomedeceleration.Inthatcase,theoverall

linearcurvemaybeseentotaperoffwithalowerslopethantheearlierpoints.Ifthesedatacomefromrunners,itcanbe

usedtodeterminehowsteadytherunnersactuallyare.Also, if therunnersstartfromzero,thefirst10yardswillshowan

upwardcurveindicatingacceleration.

Figure1-2showsexpectedresultsforthreerunsof0.5,1.0,and1.5meterspersecond(m/s).

Figure1-2Distanceversustimeforthreedifferentvelocities.

WhyItWorks

Average velocity can be thought of as the distance you go divided by the amount of time it took to get there. More

specifically,wecansayaveragevelocityisthechangeindistancedividedbythechangeintime.v=Δd/Δtistheslopeofthedistanceversustimegraph.(ΔistheGreekletterdelta,whichmeans“changein.”)

OtherThingstoTry

ThisexperimentcanbedoneusingapersonridinginstyleinaHovercraft,aspicturedinFigure1-3.Thiscanbedoneasan

interestingwaytodothepreviousexperimentorjustsimplyforthefunofdoingit.

Becauseofthenearlyfrictionlessmotion,thepersonmovesatconstantvelocityandmakesaperfectobjecttomeasure

atvariousspeeds.YoucanpurchaseaHovercraft(PASCO,partnumberME9838).

AHovercraftcanalsobebuiltbyfollowingthesebasicsteps:

1. Drillaholeinthecenterofa3-to-4footdiameterpieceofplywood.

2. Cutaholehalfwaybetweenthecenterandtheedgejustlargeenoughtofittheendofaleafblower.

21

Figure1-3Hovercraft.CourtesyPASCO.

3. StapleaplasticsheettothebottomoftheHovercraft.Trimofftheexcessplastic.

4. Insertabolt from theundersideof theHovercraft, throughaplasticspacer (made fromaplasticcoffee-can lid).

Attachtheboltthroughwashersonthetopandbottom,andthensecureitwithanut.

5. Tapeallthesealsbetweentheleafblowerandtheplywood,andtheplasticsheetandtheplywood,tomakethem

asairtightaspossible.

6. Cutseveralapproximately2-inchdiameterventholesintheplasticsheetafewinchesfromtheoutercircumference

oftheplasticspacer.

7. Withtheleafblowerturnedon,acushionofairshouldenableapersontomovewithaminimumoffriction.

Detailedplanscanbefoundathttp://amasci.com/amateur/hovercft.html.

The tendencyofamovingobject tokeepmoving iscalled inertia,which isaddressed inNewton’s first law.This is the

subjectofexperimentsthatfollow.

ThePoint

Constantvelocity is representedbyastraight lineonadistanceversus timegraph.Theslopeof the line isequal to the

averagevelocity.

22

Project2

Picturingmotion.Gettingamoveon.

TheIdea

Inthepreviousexperiment,weworkedwithconstantvelocityinonedirectionandfoundthatthemotionwasrepresentedby

simplegraphswhoseslopeswerestraight lines.Here,youstudythemotionofapersongoingforwardandback,fastand

slow.Youalsomeasure theeffectofspeedingupandslowingdown.Thesegraphswill takeonanewdimension. In this

experimentyouuseamotionsensorwithdisplaysoftwaretogetabetterfeelforwhatdifferenttypesofmotionlooklike.

Graphsareusedtoshowwhereanobjectisatvarioustimes.

WhatYouNeed

motionsensor

appropriatecomputerinterfaceforthemotionsensor

(roughly)8inchby10inchpieceofcardboard

Method

Motionsensor(PASCOEasyScreen)

1. Attach a motion sensor to your computer. If you have a PASCO motion sensor, it is connected through the

computer’s USB port by way of a computer interface. Follow the specific details provided by the sensor’s

manufacturer.

2. IfyouareusingthePASCOsensor,selecttheEasyScreentogetstarted.Fourmotionpatternswillcomeuponthe

screen.Selectonetostartwith.PressRun(whenyouareready).

3. Holdtheboardfacingthemotionsensor.(SeeFigure2-1.)

4. Positionyourselfsoyoustartatadistanceof1meterfromthescreen.Onthecomputerscreen,youseeavisual

indicatororyourpositionasafunctionoftime.

5. Adjustyourpositiontomatchthepatternonthescreen.(Note:youmightbetemptedtothinkthatmovingforwardis

positive,butthisisnotthecasehere.Movingbackwardresultsinincreasingthedistancebetweenyourselfandthe

motionsensor.Asaresult,forourpurposeshere,thisisthepositivedirection.)

6. RepeatforeachofthepatternsavailableontheEasyScreen.

23

Figure2-1Matchingapatternusingamotionsensor.CourtesyPASCO.

ExpectedResults

Figure2-2 shows the result of someonemovingbackwardand forward in suchaway that theymatch the targetmotion

pattern.Thisrepresentsholdingstillfortwosecondsat0.5metersdistance,thenmovingbackat2.2m/s,andthenholding

stillforanothertwosecondsatadistanceof1.8meters.Thepersondoingthematchingdoesnothavetothinkaboutthis,

butonlyneedstolookatthescreenandmovetofitthepattern.

Constantvelocityinthepositivedirection(whichinthiscaseisdefinedasawayfromthemotionsensor)isrepresentedby

astraightlineonadistanceversustimegraph.Thefasterthemotion,thesteepertheslope.

Figure2-2Motionmatchresults.CourtesyPASCO.

Zerovelocitymeansthedistancestaysthesameoveragiventimeinterval.Thisisrepresentedasahorizontallineonthe

distanceversustimegraph.

Acurvedlinewouldbeproducedbyacceleratedmotion(speedinguporslowingdown).

WhyItWorks

Thedistanceanobjectgoesinagiventimeinterval,t,isgivenbytheequation:

d=do+vt

24

From this equation, the slope of the distance versus time graph is given by v, the velocity of the motion. The initial

separationfromthemotionsensor,do,determineshowfarabovethebaselinethegraphstarts.

Each new phase of the motion contributes a separate segment to the graph. For instance, if the velocity stops, the

distanceremainsconstantforthatperiodoftime.Ifthemotionistowardthemotionsensorforanotherperiodoftime,that

motioncontributesasegmentofthegraphwithanegativeslopethatconnectstotheothersegments.

Table2-1summarizesthevariouspossibilities.

Table2-1

OtherThingstoTry

Atreasuremap

1. Onapieceofpaper,drawthefollowingmoves(ormakeupyourown):

Forward1meterinthreeseconds

Inplacefourseconds

Back0.5meterintwoseconds

Forward2.5metersinfourseconds

Inplacefourseconds

Back1meterinthreeseconds

2. Howfardidyouget?

Whatwasyourdisplacement?(Thisisthetotaldistanceyoutraveledfromyourstartingpoint.)

Whatwasyouraveragevelocity?This isthedisplacementdividedbythetotaltime (including the timestanding in

place).

Whatwas the totaldistanceyou traveled?Unlikedisplacement,every forwardandbackwardmovecontributes to

distance.

Whatisyouroverallspeed?Youroverallspeedisthedistancedividedbythetotaltime.Thetotaltimeisthesame

forbothofthese.

Theresultsofthetreasurehuntis:

Totaltime=20seconds

Displacementfromthestartingpoint=+1+0−0.5+2.5+0−1=2.0metersAveragevelocity=2meters/20seconds=0.1meterspersecond

Totaldistancetraveled=+1+0+0.5+1.5+0+1=4meters

Overallspeed=4meters/20seconds=0.2meterspersecond

Makeyourowndistanceversustimechallenges:

1. SelectanyoftheEasyScreenPatterns.

2. Usinga transparencymarker (erasable or not is your choice) and trace the rectangular shapedefining theEasy

25

ScreenGraph.

3. Drawyourownmotionpatternonthetransparency.

4. Tapethetransparencyonthescreen,sotherectanglealignswiththeoneyoutracedonthescreen.

5. Matchyourpatternbyadjustingyourdistanceasbefore.Thistime,youwillbeignoringtheEasyScreenPatternand

followingonlyyourown.

Once you get the hang of it, you can throw in accelerated motion. Acceleration (away from the motion sensor) is

representedbyanupwardslopingline,whichiscurvedupward.Acceleration(towardthemotionsensor)isrepresentedbya

downwardslopinglinethatiscurveddownward.

ThePoint

Constantvelocityisrepresentedbyastraightlineonthedistanceversustimegraph.Thevelocityisgivenbytheslopeofthe

line.

If thecurve is nota straight lineatanypoint this indicates thatacceleration hasoccurred.Accelerationcanbeeither

positive(speedingup)ornegative(calleddecelerationorslowingdown).

Anobjectmovinginaparticulardirection(forwardorbackward)canexperienceeitherpositiveornegativeacceleration.

26

Project3

Thetortoiseandthehare.Playingcatch-up.

TheIdea

Onecarisgoingfasterthantheother,buttheslowercarhasaheadstart.Wecanpredictwhereandwhenthefastercarwill

overtake the slower car. All we have to do is graph the movement of each car and see where the lines cross. This

experimentgivesyouamethodtomakethatprediction.

WhatYouNeed

2toycarswithadjustablespeeds

stopwatch

tapemeasure

Method

1.Setthespeedofeachofthetwocars,sooneisfasterthantheother.(Ifyoudon’tknowthespeedsbeforestarting,

youcanmeasuretheminthefollowingsteps.)

2.Determinetheaveragevelocityofeachofthecarsbymeasuringthedistanceitgoesinagivenamountoftime.The

equationisaveragevelocity=(distancetraveled)dividedby(timetogetthere).Inphysics,metersaretypicallyusedto

measure distance (to be consistent with the SI or System International unit system). This will result in velocity

measuredinmeterspersecond(m/s).However,youcanworkwithotherunitsfordistance(suchasfeetpersecond)

aslongasyouareconsistent.

3.Lineupthetwocarsinthesamedirectiononalevelfloorheadinginthesamedirection,asshowninFigure3-1.

4.Wearegoingtogivetheslowercaraheadstartofafewsecondsandtrytopredictwherethefastercarwillovertake

theslowercar.

5.Todothis:

Plotthespeedofthefastercaronagraphofdistanceversustimewiththelinestartingattheoriginandhavinga

slopeequaltothespeedofthefastercar.

Plotthespeedoftheslowercaronthesamegraph,butstartingatapointwherethedistanceiszeroandthetime

isequaltothechosentimedelay.

SeeFigure3-2,whichshowsaslowercargoingat0.25meterpersecondcargivena0.25meterheadstartinfront

ofafastercargoing0.4meterpersecond.(Noticetheslowercarispredictedtoovertakethefastercaratapoint

thatis0.68metersfromthestartingpointand1.8secondsaftertheracestarts.)

27

Figure3-1Whenwillthefastercarovertaketheslowerone?

Figure3-2Fastercarpassestheslowercarwhereandwhenlinescross.

6.Predictwherethefastercaryouareworkingwithwillovertaketheslowercar.

7.Starttheslowercarandgiveitaheadstart.

8.Comparewhereandwhenthefastercarwillovertaketheslowercarwithyourpredictions.

ExpectedResults

Thefastercarwillovertaketheslowercarwhenthetwolinesinthegraphcross.Thedistancethelinescrossatishowfar

fromthestartinglinethefastercarcatchestheslowercar.

Thetimewherethelinescrossishowmanysecondsfromthestartoftheracewhentheslowercarcatchesthefaster

car.

WhyItWorks

Thedistancethataobjectgoesisgivenbytheequation:

d=do+v(t−to)wheredoistheinitialdistancebetweenwheretheobjectstartsandthestartingline.(docanbeunderstoodastheheadstart

indistance)

visthevelocityofthecar

28

tisthetimeithasbeengoingfromthestartoftherace,andtoisthedelayortheheadstartinsecondsgiventotheother

car.

OtherThingstoTry

Herearesomealternativewaysofdoingthis:

1. If you have twomotion sensors, focusoneon the faster carand theother on the slower car.This generatesa

similarcurveasshowninFigure3-2.Ifthecarsaremovingawayfromyouasimilarcurvewillbeproduced,except

theslopewillbepositive.

2. Another way to establish two different velocities is to use objects rolling off two different slopes starting from

differentheights.Theobjectstartingfromthehigherstartingpointwillberollingonthetableorfloorwithahigher

velocity,withthevelocityproportionatetotheheightdifference.Ifthebottomsofeachoftherampsarethesame

distancefromthestartingline,theslowerrollingobjectcanbegivenafewsecondsheadstart.Asimilarprediction

andcomparisonofresultscanbemadeasintheprevioussection.

3. IfyouhappentobeassociatedwithaFIRSTroboticsteam,youmaywanttoconsiderusinglastyear’srobot(s)for

thisexperiment.

4. Anothervariationistopredictwhereandwhentwocarsmovingtowardeachotherwillmeet.

ThePoint

Twoobjects thatmove independently can be represented by separateequations that represent the relationship between

distanceandtime.Thesearetwosimultaneousequations,whichcanbesolvedgraphicallytofindthetimeanddistancethat

thefasterobjectovertakestheslowerobject.

29

Project4

Howdoesasailboatsailagainstthewind?Componentsofforce.

TheIdea

Itisnothardtounderstandhowagoodstiffwindblowingfrombehindasailboatcanmoveitalongatabriskpaceinthe

water.Butwhataboutgettingbackhome?Howcanasailboatmove(ortack)againstthewind?

Inthisproject,youdiscoverhowasailboatmovingagainstthewindcanresultinaforcethatpushesthesailboatforward.

Thisgetstotheideaofhowaforceinonedirectioncanbebrokendownintoseparatecomponentforces.Twomethodsare

shownhere.Thefirstmethodusesasailattachedtoapulleyonastring.Thesecondmethodusesanairtrackforthose

readerswhohaveaccesstoone.Afterlookingatthesemethods,youareencouragedtotryoneorbothofthese,ortocome

upwithyourownidea.

WhatYouNeed

Pulleyandstring:

stiffpieceoffoamboardorcardboardtouseasasail

(low-friction)pulley

smallmasswithanattachmenthook,approximately20g

1–2metersofthinstring

attachmentpoints(suchasringstandsclampedtoalabtable)toholdthestringhorizontally

blowdryerorothersourceofairflow

ducttape

Airtrack:

airtrack

glider

attachmentfor theglider thatcanholda“sail.”Abumper, for instance,canbeattachedto the topofaglider to

30

serveasa“mast.”

1CD(orastiffsheetofcardboard)

Method

Pulleyandstring

1. Attach thestringhorizontally to twoanchorpoints.Thestringshouldbe tautandable to supporta smallweight

withoutsagging.

2. Hangthepulleyonthestring.

3. Hangtheweightonthepulleysothepulleyisfreetoslideonthestring.

4. Tapethefoamboardorcardboardatanangleofabout20–30degreeswithrespecttothedirectionofthestring.

5. With thesailboatsupportedon thestring,direct theblowdryerat thesail.Theblowdryershouldbeataslightly

greaterangle(withrespecttothestring)thantheangleofthesail.Iftheairfromtheblowdryeristoostrong,the

sailmayvibrate. If theangle istoosmall, thesailwillbeforcedbackwardwiththewind.However,undertheright

conditions,theforceintheforwarddirectionwillbestrongenoughtopropelthepulleyagainstthewind,inasimilar

mannertoarealsailboat.SeeFigure4-1.

Airtrack

1. Level the air track. You can determine that the air track is level by observing the glider when the air track is

activated.Ifthegliderdoesnotmoveineitherdirectionundertheforceofgravity,thenthetrackcanbeconsidered

tobelevel.

2. Attachafixtureonthegliderthatcanholdaflatobject,suchasaCD.

3. PlacetheCDintheholderandsecureitatanangleofabout20–30degreeswithrespecttotheairtrack.

4. Direct the blow dryer at a slightly greater angle than the angle of the sail, and then observe its response. See

Figures4-2and4-3.

31

Figure4-1Atthecorrectangle,theblowdryerwilldrawthefoamboardsailintothewind.

ExpectedResults

Foreithermethod,theactionoftheblowdryerifpositionedproperlycausesthe“boat”tomovetowardtheblowdryer.The

boat isseen tomove“against thewind.”Theparallelcomponentof the forcewillcause thesailboat tomoveforwardor

tackingagainstthewind.

Using thepulley, ifconditionsare right, theperpendicularcomponentof the forcewillalsocause thesailboat to rotate

aroundthestring.This iscomparabletoasailboat listingundertheforceofastrongwind.Thekeelofanactualsailboat

servestocounteracttheeffectofthisperpendicularforce.Inthisexperiment,thisforceisnotconstrainedandcausesthe

pulleytorotate.

32

Figure4-2Sailboatsimulationusinganairtrackviewedfromtheside.PhotobyS.Grabowski.

Figure4-3Sailboatsimulationusinganairtrackviewedfromthetop.PhotobyS.Grabowski.

WhyItWorks

Thephysicalstructureofasailboatneedstodoatleastthreethings:

1.Itpicksuptheforceofthewind(roughly)perpendiculartothesail.

2.Thekeelof thesailboatmakesthesailboatfollowone-dimensionalmotionbypreventingthesailboatfromslipping

perpendiculartoitsforwardmovement.

33

Figure4-4Forcesonasailboat.

3.Itseparatestheforceofthewindintotwoparts:oneperpendiculartothemovementoftheboat,whichisresistedby

thekeel,andoneparalleltothemotionoftheboat,whichpropelsitforward.

Figure4-4showshowtheforcesareseparatedintotwocomponents.Theforceproducedonthesailbythewindblowing

getssplitupbythesailboatintotwootherforces.Onetriestopushtheboatsidewaysandisresistedbythekeel.Theother

force—iftheanglesareright—triestopushtheboatforward.Thishappensevenifthewindiscomingmorefrominfrontthan

frombehind.Quantitiesinphysicsthatcanbebrokendownintocomponentsasthisforceonasailboatarecalledvectors.

OtherThingstoTry

Attachingafoamboardorcardboardsail toatoycarwillwork.Thewheelsofthecarmustturnfreelyandthetiresmust

haveenoughfrictiontoserveasa“keel”torestrictsidewaysmotion.

Anotherway to do this is to usea (nearly) frictionless hockey puckwith a low-friction tube to constrainmotion in one

dimension.Aguidestring(suchasfishingline)isusedtokeepthemotioninonedimension.Youhavetokeepenoughtension

onthestringtopreventthepuckfromrotatingandbinding.Thepuckmustalsobeonanearlyperfectlyhorizontalsurface.

Tape a sail as in either of the two methods previously described. This approach also requires a reasonably horizontal

surfacetopreventthepuckfromdriftingonitsownbeforethebloweristurnedon.

ThePoint

Aforceinonedirectioncanbethoughtofasbeingequivalenttotwootherforcespushingincompletelydifferentdirections.

Thishappensbecauseforceisavectorquantityinphysics.Thisprojectillustrateshowaforceonthesailofasailboatisthe

sameasasidewaysforcepushingagainstthekeelandaforceintheforwarddirectionofthesailboat.Thisisanexampleof

theresolutionofaforceintotwoperpendicularcomponents.

34

Project5

Steppingonthegas.

TheIdea

Pressingdownwithyourfootontheacceleratorofacardoesnotnecessarilycauseyoutoaccelerate.Youmaybemoving

forwardwithconstantvelocity.Howcanyoutellifyouareaccelerating?Thisexperimentshowsyouafewwaystodetermine

whetheryouareacceleratingorjustmovingalongatconstantvelocity.

Inthisproject,youcanalsofindwaystodetectcentripetalacceleration,whichkeepsthingsmovinginacircle.

WhatYouNeed

Anyorallofthefollowing“accelerometers”canbeusedtodetectacceleration:

pendulum:anyweightonastring

floattiedtoastringheldunderwater

candle

partiallyfilledtankofliquid

accelerometer,suchasshowninFigure5-1

Figure5-1Accelerometer.CourtesyPASCO.

Method

Pendulum

1. Holdingthestringofthependulum,moveatassteadyapaceasyoucan.Observethependulumduringconstant

velocity.

2. Nowdothesamething,butobservewhathappenswhenyouspeedup(accelerate).

Skateboardaccelerometer

1. Attachapendulumtoaskateboard,asshowninFigure5-2.

2. Rollitdownarampthathasalargeenoughslopefortheskateboardtoincreaseitsspeed.Observetheanglethe

35

pendulummakeswiththeverticalposition.

3. Adjust theslopeof the ramp, so theskateboard is just heldon the rampby frictionwithout slidingdown.This is

calledtheangleofrepose.

4. Givetheskateboardaslightnudge.Itshouldmoveatafairlyconstantvelocity.Notetheangleofthependulum.

5. Whathappensiftheskateboardslowsorgoesuparamp?

Centripetalacceleration

Spinanapparatus,suchasshowninFigure5-3or5-4.Apairofcandlesateitherendofaspinningboardisanotherwayto

dothis.Thefloatingbobapparatus iscommerciallyavailableorcanbeassembledfromfishingbobs(orStyrofoamballs),

babyfoodjars,apieceofwoodwithaholeinthecenter,andametalpost.

Figure5-2“Skateboard”accelerometer.

ExpectedResults

Apendulumhangsverticallywhenmovingatconstantvelocity.Butitmovesintheoppositedirectionastheaccelerationitis

experiencing.Ifanobjectslowsdownordecelerates,itshowsupasabackwardmovementinthependulum.

Figure5-3Floatingbobaccelerometer.

Whentheapparatuswiththefloatingbobisspinning,thebobmovesinward.Thismaybetheoppositeofwhatyoumight

expect and is the opposite ofwhatwould happenwith a freely hanging pendulum.The reason for this is the centripetal

acceleration increasesthebuoyantforceonthebob,forcing it inward.Candlesmove intheoppositedirection.Theflame

36

movesoutward,asdoesliquidinacontainer.

WhyItWorks

Newton’ssecondlawrequiresthatforceandaccelerationarerelatedtoeachotherthroughF=ma.Ifthereisacceleration

(a),thereisaforce(F)onthemovingobject(ormass,m).Theforceisinthesamedirectionastheacceleration.

OtherThingstoTry

Anaccelerometer,suchasshowninFigure5-4,directlyindicatesaccelerationwithasetofLEDsthatlightinproportionto

the amount of acceleration. The greater the acceleration, the more LEDs will light. It can, for instance, indicate the

accelerationofacartpulledbyastring.Itcanalsobeusedtomonitorcentripetalacceleration.

ThePoint

Ahanging(orotherunconstrained)objectisaffectedbyacceleration,butisnotaffectedbyuniformsteadyvelocity.

Figure5-4Anappliedforcecausesanobjecttoaccelerate.CourtesyPASCO.

37

Project6

Rollingdownhill.Measuringacceleration.

TheIdea

Whenexposedtotheforceofgravity,objectsfallfasterandfaster.Thisiscalledgravitationalacceleration.Whenobjects

fallstraightdown,youhavetobeveryquickifyouwanttomeasurehowlonganobjectfallsagivendistance.WhenGalileo

Galileitriedtodothisduringthefifteenthcentury,heusedprimitivetimingdevices,suchasdrippingwaterandhisownpulse

tokeeptrackofobjectsdroppedfromtheLeaningTowerofPisa.Toovercomethedifficultyoftimingthesemeasurements,

Galileo had the brilliant insight of slowing down gravitational acceleration using a ramp. In this experiment, you follow in

Galileo’sfootsteps.However,youhavetheadvantageofbeingabletouseastopwatchorevenamotionsensortomore

accuratelymeasuretheobject’smovement.

WhatYouNeed

inclinedtrack(suchasasectionofwoodencornermolding,semi-roundvinylbullnosemolding,oraflatboardwith

two“gutters”createdbyattachingmetersticksasguides)

golfballsormarbles

stopwatchorothertimer

meterstick

optional:motionsensor,inclinedairtrack

Method

1.Settheinclinedtrackatamoderateanglewithrespecttothesurfaceonwhichitissupported.

2.Markdistanceintervalsfromthebottomofthetrackin10cmincrements.

3.Releasethegolfball(ormarble)fromeachofthedistancesmarkedandrecordthetimeinsecondsthatittakesto

reachtheendoftheramp.SeeFigure6-1.

Figure6-1Rampusedtomeasureeffectsofacceleration.

4.Ifyoumeasurethedistancetheballrollsandthetimeittakestoroll,youcaneasilyfindtheacceleration,a,atany

pointusinga=2d/t2,wheredisthedistanceitrollsandtisthetimeittakestorollthatdistance.

5.Whatistheeffectofchangingtheslopeoftheinclineontherateofacceleration?

ExpectedResults

Agraphofdistanceversustime,suchaspicturedinFigure6-2,showsthatthedistancetheobjectmovesinagivenamount

38

oftimeisincreasing.Thedistanceinthegraphisshowntoincreaseasthesquareofthetimewhichisacharacteristicof

constantacceleration.

WhyItWorks

Whenanobjectaccelerates,itsvelocitychangeswithtime.Forthecaseofconstantacceleration,thevelocityincreasesby

aconstantamounteverysecond.Thisresultsinthedistanceincreasingasthesquareofthetime.

OtherThingstoTry

A rolling golf ball or marble can be considered a falling object whose acceleration is slowed by the incline. This is

approximately,butnotcompletely,true.Anyrollingobjectdevelopsangularmomentumthattiesupsomeofitsenergyinthe

processofrolling.

Figure6-2Distanceversustimeforagolfballrollingdownanincline.

Figure6-3Anairtrackwithamotionsensorattachedtotheend.CourtesyPASCO.

Betterprecisioncanbeachievedbyusinganairtrack.Thisreducesthe impactoffrictionandrotationalkineticenergy.

Incorporatingamotionsensortomeasurevelocityandaccelerationaddsanotherdimension,asFigure6-3shows.

DataStudiosoftwaredisplaysthedistancemeasuredbythemotionsensor,asshowninFigure6-4.

ThePoint

Whenanobjectaccelerates,itsvelocitychangeswithtime.Ifthataccelerationisconstant,distanceincreasesasthesquare

oftime.

39

Figure6-4Position(inmeters)versustime(inseconds)forthreedifferentinclines.CourtesyPASCO.

40

Project7

Independenceofhorizontalandverticalmotion.Basketballtossedfromarollingchair.

TheIdea

Whichwillhit thegroundfirst:abulletdroppedstraightdownfromaheightof5feetorabulletfiredhorizontallyoverflat

groundat300m/sfromthesameheight?Manypeopleguessthatthegreatermomentumofthemovingbulletwouldkeepit

intheairlonger.Thisexperimentaddressesthisquestion.

Aprojectile isanobjectthathasbothhorizontalandverticalmotion.Althoughmotion intwodimensionsmayseemvery

complicated,itcanbeenormouslysimplifiedbasedontheresultsofthissection.Youdiscoverthatthehorizontalmotionofa

projectileiscompletelyindependentofitsverticalmotion.Itdoesnotmatterhowfastanobjectisfalling.Inthisexperiment,

youprovethisinseveralways.

WhatYouNeed

chair

basketball

someonewillingtositinachair

independenceofhorizontalandverticalmotionapparatus

ballisticcar

Method

Rollingchair

Thisissimpletodo,butithasasignificantresult.

1. Havethepersonsitinthechairholdingthebasketball.

2. Rollthechair(withthepersonsitting).Thepersoncanalternativelybeonaskateboardorrollerblades.

3. Havethepersontossthebasketballupandobserveitstrajectory.

Coins

1. Placeacoinattheedgeofatable.

2. Flickasecondcointowardthefirstsothatthefirstisjustpushedovertheedgeandthesecondcoinfliesoffthe

table.

3. Bothcoinsshouldstartfallingatthesametime.Onewithahorizontalvelocityandonewithout.

4. Listen to seewhich, if any of the coins, strikes the floor first. Repeat this enough times until you get consistent

results.

Apparatus

Useacommerciallyavailableapparatus,suchaspicturedinFigures7-1and7-2.TheapparatusshowninFigure7-1ismuch

easiertouse.TheballisticscarshowninFigure7-2mayrequirealevelsurfaceandsomepractice.Amorereliableversion

ofthisisavailableasanaccessoryforanairtrack.

41

Figure7-1Bothballshittheflooratthesametime.

ExpectedResults

Thebasketballshouldgoupandcomedowntobecaughtbythepassengerintherollingchair.Thisworksbestiftheballis

thrownstraightupintheverticaldirection.Similarly,thecoinswillhitthegroundatthesametime.Itiseasiertocomparethe

soundofthecoinsstrikingthefloorthantomakethatcomparisonvisually.Whenusingacommercialapparatus,agreater

distancefromthefloorgivesamoredefinitiveresult.

WhyItWorks

Theforceofgravityanditsassociatedaccelerationisentirelyintheverticaldirection.Gravitydoesnotinanywayinfluence

thehorizontalvelocity.

Figure7-2Ballisticscarshowingthesteelballhasthesamehorizontalvelocityasthecar.

OtherThingstoTry

42

1. Placeacoinattheedgeofatable.

2. Slideasimilarcointowardthefirstone,sothemovingcoinjustknocksthestationarycoinoffthetableandbothfall

tothefloor.Thiswilloccurifthemovingcoinstrikesthestationarycoinatalargeenoughangle.

3. Ifaproperangle ischosen,thestationarycoin isnudgedoffthetableandfallsnearlystraightdown.Themoving

coinwillfallatagreaterdistancethanthestationarycoin.

ThePoint

Horizontalmotionandverticalmotionarecompletely independent.Excluding theeffectsofair resistance, thehorizontally

firedbulletwillfalltothegroundatexactlythesametimeasthedroppedbullet.Thisformsthebasisforanunderstandingof

projectilemotionthatisgreatlysimplifiedbytreatingtheverticalandhorizontalmotionseparately,asiftheotherdidnoteven

exist.

43

Project8

Targetpractice.Horizontalprojectile—rollingoffatable.

TheIdea

Inthisexperiment,youwilltrytohitatarget.But,toimproveyourodds,youcanusethelawsofphysicstopredictwherea

projectilewill land.Yourprojectilewillbeasteelballoramarble.Thephysicalsituation isverymuchsimplifiedwhen the

projectile isshot (or launched) in thehorizontaldirectiononly. In thisproject,weseehowcloseyoucanget to the target

usingthelawsofphysicsthatdescribehowhorizontalobjectsmoveundertheforceofgravity.

WhatYouNeed

steelballormarble(toserveasaprojectile)

inclinedtracktogetthemarblerolling(Thiscanbeapieceofgroovedwoodenmoldingorarulerwithagroove)

flat,smooth,horizontaltable

stopwatchorothertimer(wristwatch,cellphone)

cup(yourtarget)

meterstick

optional:motionsensor(tomeasurevelocity)

Method

Part1:Findthevelocityofthemarblecomingofftheramp

Youwillneedthisinformationtomakeyourpredictions.

1. Setuptherampinsuchawaythatitspositionremainsfixed.

2. Placeamarbleatthetop(oranotherarbitrarilymark)oftheramp.

3. Releasethemarblefromthemarkandmeasurethetimeittakestogotothebottomoftheramp.

4. Repeatafewtimesuntilyougetaconsistentreading.Then,taketheaverage.(Iftherampistooshortortheslope

istoogreat,itismoredifficulttomeasurethetimetogodowntheramp.)

5. Findthefinalvelocityatthebottomoftherampusingtheequation:

Part2

1.AswefoundinProject5,theverticalmotionisindependentofthehorizontal,sowecandeterminethetimeittakes

themarbletofallfromthetablejustfromtheheight,h,ofthetable.Thisisgivenbytheequation:

2.NowmakeyourpredictionforhowfarthemarblewillgousingR=vt.ThedistancetheballwillgoisnowgivenbyR=

vt.UsethevyoufiguredinStep5aboveandtfromthepreviousstep.

3.Setthe(centerofthe)cupatthedistanceyoupredictedandtryitout.Nocheating.Itismorefuntocallyourshotfirst,

andthenseeifitworks.Linethecupupvisually,soitisonastraightlinewiththemotionofthemarble,asshownin

44

Figure8-1.

ExpectedResults

Clearlytheexpectedresultisforyoutohavethemarblerollintothecup.Ifthemarblehitsataboutthedistanceofthecup,

buttotheleftorright,thatshouldcountasahit.Hittingthetargetrequiresaccuratemeasurementofthemarble’svelocityon

thetable.Itisreasonabletoassumethatthemarbledoesnothaveanysignificantvelocitylossfortheshorttimeitisrolling

onthetable.

(Asimplerwayofdoingthis—appropriateforyounger readers—istoqualitativelycompare thedistancethemarblegoes

withtheheightoftherampandskippingthemath.Thehighertheramp,thefasterthemarbleandthefartheritgoes.)

Thetimeittakestofallfromagivendistanceisprovidedbytheequation:

Tousethisequation,thedistancetheprojectilefallsmustbecompatiblewiththeunitsforgravitationalacceleration,g. If

youuse9.8m/s2forg,hmustbeinmeters.ThetimetofallagivendistanceisshowninthefollowingTable8-1:

Table8-1

Usingthistable,thedistancetheprojectilegoesissimplyitsvelocitymultipliedbythetimeitisintheair(fromthetableor

equation).

WhyItWorks

Thehorizontalvelocityofthemarbleisconstantandunaffectedbythefactthatthemarbleisfalling.Thedistanceitmoves

issimplythehorizontalvelocitymultipliedbythetime.

Thetimeittakestofallagivendistanceisdependentonlyontheverticaldistance.

Findthevelocityatthebottomofarampusingthefactthatthefinalvelocityistwicetheaveragevelocitydividedbythe

time.

45

Figure8-1Horizontalprojectile.

Thehorizontaldistancethemarblegoesissimplythehorizontalvelocitytimesthetime.

OtherThingstoTry

Anotherwaytodothisistouseahorizontalprojectilelauncherandcalibratethevelocity.

ThePoint

Horizontalmotionandverticalmotionarecompletelyindependent.Thismeanswhenanobjectismovingwithonlyaninitial

horizontalvelocity,thetimeitisintheaircanbedeterminedbyhowlongittakestofall.

46

Project9

Takingaim.Shootingaprojectileatatarget.

TheIdea

Inthisexperiment,yougettoshootthingsaroundtheroom.Youcanuseatoybow-and-arrow,atoyping-pongballshooter,a

Nerfgun,amarble launcher,oraprecisionprojectile launchermade for thispurpose.You learn tomakepredictions that

accuratelyguidetheprojectiletothetarget.Inthiscase,usingthelawsofphysicsisnotcheating.Itdoes,however,giveyou

adefiniteadvantagecomparedwithsomeonewhoisnotarmedwiththisknowledge.

First,youmeasurewhatisthebestangletoaimsomethingforittotravelthegreatestdistance.

Then,youmakeandtestpredictions.Tohitatarget,youneedtoknowonlytwothings:thevelocityoftheprojectileandthe

angleatwhichitisshot.That’sall.Knowingonlythosetwoconditions,youcandeterminehowfartheprojectilewillgo,and

howhighitwillgo.Theangleiseasytomeasuredirectly,sowewillfirstworkonasimplewaytodeterminethevelocity.

WhatYouNeed

projectileandlauncher

–Aprojectilelauncher,suchasshowninFigure9-1.Plasticratherthansteelballsaresafer.

–Or,atoygun,atoybow-and-arrow,aping-pongballshooter,Nerfgun,oramarblelauncher.

tapemeasure

protractor

target—horizontal:panorcup;vertical:ringonaringstand

stool(s)orothermoveableobjecttoholdthetargetattheheightofthelauncher

Method

Whatisthebestangle?

Westartherebecausethispartdoesnotinvolveanynumbercrunching.

1.Youwillbeshootingyourprojectilefromground-to-groundorfromtabletoptoraisedsurfaceatthesameheightas

thetabletop.Theprojectileshouldbelaunchedandlandatthesameheight.

2.Selectasettingforyourlauncherthatwillfireaprojectilefromagivenheightandreturntothatsameheightwithout

hittingtheceiling,awall,orbreakinganything.

47

Figure9-1Projectilelauncher.CourtesyPASCO.

3.Forevery test in thispart, youwillbeusing thesamevelocity.Pickanangle toshoot theprojectileat.Launch the

projectile andmeasure the distance. Increaseor decrease the launchangle until you find theangle that gives the

greatestdistance.(Remember,forthispart,wearemeasuringthedistancetheobjectgoesafterreturningtothesame

heightfromwhichitwaslaunched.)

Determinethevelocityofthelauncher(tomakepredictions).

Forthispart,wearegoingtousethemethodoftheprevioussectiontodeterminehowfasttheprojectileismovingasit

leavesthelauncher.Forthispartonly,weshoottheprojectilehorizontally,sowecanfindthisvelocity.

1. Firehorizontallyseveraltimesandrecordthedistance,R,thattheprojectiletravels(inm).Taketheaverage.

2. Measuretheheightwhentheprojectileleavesthetable.

3. Aswedidinthepreviousexperiment,wewillusethetrickoffindingthetimetheprojectileisinflightbydetermining

howlong it takestofall.Thiscanbesimplyfound justknowingtheheight (inmeters)andusingtheequation, t=

(2d/g)½,wheregis9.8m/s2.Table8-1intheprevioussectiongivesthetime,t,forvariousheights.

4. Now, it isasimplemattertofindthevelocityusing the techniqueof theprevioussection.Divide thedistance the

objectgoesalongthefloor,R(inmeters),bythetimeitwasinflight,t(seconds).Thisisgivenbytheformula:

v=R/t

Hittingthetarget

1.Selectanangle,θ,atwhichyouwillshoottheprojectile.2.Predicttherange,orhowfartheprojectilegoesalongthefloor,usingtheequation

R=(v2/g)sin2θwherevisthevelocityyoujustfoundinnumber4,gis9.8m/s2,andθistheangleyouselected.3.Predicttheheightusingh=(vsinθ)2/2g,withthevariablesasdefinedinthepreviousequation.4.SetacupadistanceRhorizontallyalongthegroundlocatedatthesameheightasthelauncher.

5.Setaringontopofaringstandataheight,h,abovethelevelofthelauncher.Thecircularopeningoftheringshould

befacingthelauncher.Useafewstools(stackedontopofeachother,ifnecessary)tosettheringstandtoestablish

theheighttarget.

6.Visuallyalignthetargets,sotheyareinlinewiththeprojectile.

7.Afteryousetthetargetstowhereyoupredictedtheyshouldbe,firethelauncherandseehowcloseyouget.

ExpectedResults

48

Figure9-2showstypicalresultsforaprojectilefiredatavelocityof10meterspersecond.Noticethatthe45-degreeangle

resultsinthelongestrange.Noticealsothatthe60-degreeand30-degreeangleswindupinthesameplace.Theprojectile

firedat75degreesstaysintheairlonger,butithasalowerhorizontalvelocitythantheonefiredat30degrees.

Figure9-2Projectileshotat10m/s,returningtothesameheightitwasshotfrom.

WhyItWorks

Accordingtotherangeequation:

a45-degreeanglegivesthegreatestdistanceanobjectmoveshorizontallyalongtheground.Foragivenlaunchvelocityand

achosenangle,therangeaprojectilewillgocanbedetermined.

Similarly,theheightequation

determinesthemaximumheightofaprojectile,giventhelaunchvelocityandthechosenangle.

OtherThingstoTry

Combiningprojectilemotionwith“thermodynamics:”OK.Thejustificationfordoingthis,otherthanforfun,isastretch.Butit

doesaddabitofextraexcitementtothisexperiment.Todothis,firstofall,findaverysafeplaceawayfromceilings,loose

paper,oranyflammableobject.Nothingflammableshouldbeunderneaththeringincaseofdrips.Wraptheringwithasmall

amountof tissuepaperandsoak it ina littlealcohol.Bycarefully igniting the ring,youcanshoot theprojectile througha

flamingring.Carefulmeans:wearsafetyglasses,usealongwoodenmatch,andmakesurethatneitheryounoranyviewers

comeincontactwiththeflameortheringimmediatelyafteritburnsbecauseitcanremainhotforashortwhile.Thiscanbe

madeevenmoredramaticinaverycornywaybyplayingarecordingofJohnnyCash’s“RingofFire.”Thismustbedoneina

safeplaceandunderthesupervisionofanadult(ifyouarenotyetanadult).Bytheway,thisexperimentdoesworkperfectly

wellwithanonflamingring.

49

Figure9-3T.Dragoiushowsthe“ringoffire”top-of-trajectorytargetforaprojectileshotatanangle.

Anothermuchsimplerbutlessaccuratewaytolaunchaprojectilewithaknownvelocityatapredictableangleistodropa

bouncyballfromaconsistentheightfromanincline.Theballwillcomeoffatvariousangles,dependingontheslopeofthe

board.Asa result of conservationofmechanical energy, if released from thesameheightabove theboard, theballwill

bounceoffatthesamevelocity.Thismaynotgoasfar,butitprovidesalowercostoptiontoproduceareasonablyconstant

velocityatvariousangles.

ThePoint

Therangeandheightofaprojectilecanbedeterminedfromknowingonlythefollowingtwothings:velocityoftheprojectile

andtheanglethatitislaunchedfrom.

50

Project10

Mondaynightfootball.Trackingthetrajectory.

TheIdea

Thisexperimentwilltakeyououtsidetomakethesemeasurements.YoucanalsocollectdatafromMondaynightfootball.

Themeasurementpartisverysimple.Allyouneedtomeasureisthetotaltimeaballorotherprojectileisintheairandthe

total distancealong theground that the projectile travels. If wemeasure only those two thingswe can figure just about

everythingelse:launchangle,velocity,andheight.

Howhighdidthepuntgo?Howhardwastheballhit?Whatanglediditgo?Youkickasoccerball,hitagolfball,andpunt

afootball.Whichhasthegreatervelocity?Withoutresortingtoahigh-techsolution,suchasaradargun,thereisasimple

waytoanswerthatquestionusingonlythelawsofmotion.

Todothis,youeitherworkthecalculationsorusethetablesasaguide—yourchoice.

WhatYouNeed

stopwatch

footballfield

TVtunedtoafootballorbaseballgame

assortedprojectilesandlaunchers:soccerballorfootball;tennisballandracket;golfclubandball

Method

Projectile

1. Launchtheprojectileand,attheexactsametime,startthestopwatch.

2. Recordhowfartheobjectgoesandhowlongitwasintheair.

Calculation

Ifthissectioncontainsmoremaththanyoucaretodo,fastforwarddirectlytothetablesinthenextsection.

Figure10-1showsapuntedfootballfromtheeyesofaphysicist.

1.Findthehorizontalvelocity(inm/s),vx,bydividingtheoveralldistance,R,bythetotaltime(hangtime,t).

vx=R/t

51

Figure10-1Distance,height,velocity,andangleforafootball.

2. Find the vertical velocity (inm/s) bymultiplying one half of the hang time (or the time to reach the peak) by the

gravitationalconstant:

wheregis9.8m/s2.

3.Findthevelocity(inm/s)using:

4.Findtheangleusing:

(Incaseyoudon’tknowwhattan−1isyoucanjustusethekeyonyourcalculatorwiththatidentification.Thefunction,tan−1,alsocalledthearctan,givestheangleifyouhavethetangentofthatangle.Youcangetthetangentbydividingvybyvx.)

Find(orlookup)thevelocity,heightreached,andanglelaunched.

ExpectedResults

SeeTables10-1to10-3.

Table10-1

Howfastitgoes(inm/s)

52

Table10-2

Howhighitgets(inm)

Table10-3

Whatangleitgoesoffat(indegrees).Calculationsarebasedonθ=tan−1(vy/vx)

WhyItWorks

Thisworksforthesamereasonsasthepreviousexperiment.Becausehorizontalandverticalmotionareindependent,the

rangeandtimeintheaircanuniquelybedeterminedbythevelocity,height,andlaunchangle.

OtherThingstoTry

Determinethevelocity,maximumheight,andangleforthefollowingcases:

53

Theresultsareshowninthefollowingtable:

ThePoint

Knowingonlythetimeaprojectileisintheairandthedistancealongthegroundthatittravels,itispossibletodeterminethe

velocity,maximumheight,andangleoftheprojectile.

54

Project11

Monkeyandcoconut.

TheIdea

Amonkeyishangingfromabranchinatree.Themonkeylookshungryandyouwanttothrowacoconuttohim.However,the

monkeyisnervousand,assoonasheseessomethingbeingthrownathim,heletsgoofthebranch.(Themonkeyapparently

knows that in previous versions of this problem, a hunter was trying to shoot it, so themonkey is understandably a bit

nervous.)Knowingthemonkeywillletgoassoonasthecoconutisthrown,whereshouldyouaim?a)Abovethemonkeyb)At

themonkeyc)Belowthemonkey.

WhatYouNeed

“monkey”—(representedbyapiepanorlidofametalcontainer).SeeFigure11-1.

“coconut”—(representedbyaprojectilefromProject8)

DCpowersupply

electromagnet

insulatedwire—about25feet

switch that opens the circuit at the precise moment the projectile is launched. This can be accomplished by

assemblingtwopiecesofmetalfoilinfrontofthelauncher.Attheinstanttheprojectileemerges,itpushesthefoil

apart,openingthecircuit.SeeFigure11-2forasimplewaytosetthisup.Therearealsoopticaltechniquestodo

this,someofwhicharecommerciallyavailable.

55

Figure11-1The“monkey”:ametallidheldbyanelectromagnetattachedtoaverticalpieceofwood.

56

Figure11-2The“coconut”isshotbyaPASCOlauncherwithanaluminum-foilswitchtapedinfront.

laserpointer

varioustypesofthemonkeyandcoconutapparatusarealsoavailablecommercially

Method

1. Setuptheapparatus,asshowninFigure11-3.

2. ApplytheDCvoltagetotheelectromagnetcircuit.

3. Armthelauncher(bypushingtheballinwiththeplungerinthecaseofthePASCOlauncher).

4. Closetheswitch.

5. Aimthelauncherdirectlyatthetarget,eithervisuallyoraidedbythelaserpointer.

6. Shoottheprojectile.Astheprojectileemergesfromthelauncher,itcausestheswitchtoopenanddeactivatesthe

electromagnet.Thisreleasesthemetallid(monkey)astheprojectileisshotatit.

57

Figure11-3Electricalconnectionsforthemonkey-and-coconutapparatus.

ExpectedResults

Theanswertothequestionposedpreviouslyis:b)firingatthemonkey.Aslongasthemonkeyisinrange,firingdirectlyat

themonkeywillcauseadirecthiteverytime.

WhyItWorks

Boththemonkeyandthecoconutaresubjectedtothesamegravitationalacceleration.Ifthecoconutisaimeddirectlyatthe

monkey in the tree, thecoconutwill fall fromthatstraight linepathand follow thecurved (parabolic)path thatprojectiles

normallytake.SeeFigure11-4.Asaresult,thecoconutfallsawayfromthatstraight-linepathatpreciselythesamerateas

themonkeyfallsdownward.Thiscausesthemonkeyandthecoconuttobeinthesameplacebeforethemonkeyhitsthe

ground.

OtherThingstoTry

Supposeourmonkeygetstiredofhavingcoconutsthrownathim.Whereshouldheaimacoconutofhisownthathethrows

to deflect the one that is thrown at him? This can be set up using two projectile launchers, but it requiresmuchmore

precisionbecausetheballshaveasmalldiameter.Theanswer isthesameasthepreviousone.Themonkeyshouldaim

directlyatthehunter.

58

Figure11-4Youaimdirectlyatthemonkey.Hewillfallasfastasthecoconutandwillcatchitonthewaydown.

ThePoint

This project illustrates one of the underlying concepts of projectiles, which is the idea that the horizontal and vertical

componentsofmotionarecompletelyindependentanddonotinfluenceeachother.Themonkeydoesnothavehorizontal

motion,butthecoconutdoes.Theybothhaveverticalmotion,whichexperiencesthesamerateofacceleration,regardless

ofthehorizontalmotion.

59

Section2

GoingAroundinCircles

Project12

Whatisthedirectionofasatellite’svelocity?

TheIdea

What is thedirectionofanobjectmoving inacircle?Acommonmisconception is that thevelocity,atanygiven time, is

pointedinacircle.Thissimpleexperimentillustratesthatthedirectionofanobjectmovinginacircularpathisinastraight

line,asshowninFigure12-1.

WhatYouNeed

1marble

rollofmaskingtape

Figure12-1Thevelocityofanobjectincircularmotionatanygiventimeisastraightlinetangenttothecircle.

Method

Marbleandtapering

1. Placethemarbleinthecenterofataperoll.

2. Getthemarblespinningrapidlyinacircularpath,asshowninFigure12-2.

3. Quicklyliftthemaskingtaperollandobservethepaththemarbletakeswhenit’snolongerconstrainedbythetape,

asFigure12-3shows.

ExpectedResults

Themarblestravelinastraightpathassoonastheyarereleasedfromtherolloftape.

60

Figure12-2Marblekeptinacircularpathbycentripetalforcefromataperoll.

WhyItWorks

Circularmotionistheresultofacentripetalforcethatchangesthedirectionofmotionfromastraightlinepathtoacircular

path.Thecentripetalforceisprovidedbythestringinthecaseoftheball,bytheinteriorwallofthemaskingtapeinthecase

oftherotatingmarble,andbygravityinthecaseofsatellitesandplanets.Objectstravelinginacircleatanygiventimehave

an instantaneous velocity that heads in a perfectly straight line. This is actually a consequence of Newton’s first law of

motion,whichweexplore later:anobject inmotion tends tostay inmotion inastraight line,unless it’sacteduponbyan

externalforce.

Figure12-3Freemarblemovingalongastraightpath.

OtherThingstoTry

Attachastringtoaballandspintheballinacircle.Cutthestringorletthestringgoandobservethepathoftheballafterit

isreleased.Withoutthecentripetalforceprovidedbythestring,theballmovesinastraightline.

ThePoint

Anobjectmovinginacirclehasavelocitythattakesitinastraightlineatanygivenpointintime.Acentripetalforcethat

continuouslychangesthedirectionisneededtoformthecircularpath.

61

Project13

Centripetalforce.Whatisthestringthatkeepstheplanetsinorbit?

TheIdea

Inthisexperiment,youinvestigatehowobjectsmoveinacircle.Gravitationalforcekeepstheplanetsandsatellitesintheir

orbits.Thesamephysicallawsdeterminehowarubberstopperonastringmovesinacircle.

WhatYouNeed

1.5meteroflight,strongstring

1rubberstopper(1or2holes)

glass,plastic,orsmoothcardboardtube—about5inchesin lengthwithasmalldiameter,but largeenoughforthe

stringtomovethroughfreely

springscale—10N

clamptoattachthespringbalancetothetable

hookedmasses:10,20,50,100g

meterstick

markerpen

safetygoggles—(youwillbeswirlinganobjectinacircle,sosafetygogglesshouldbeworntopreventthepossibility

ofeyeinjury)

Method

SetuptheapparatusasshowninFigure13-1.

1. Tiethestringsecurelytotherubberstopper.

2. Feedthestringthroughtheglassorcardboardtube.

3. Withabout1meterofstringlengthbetweenthetubeandtherubberstopper,cutthestring,soabout25centimeters

ofstringisbelowthetube.

Makingmeasurements

Eachoftheseexperimentsusesthesamebasictechnique.Gettingthehangofitmaytakealittlepractice.

1.Putonyoursafetyglasses.(Thespinningwasherposesapotentialeyehazard.)

2.Youhavetwowaystomeasurethecentripetalforcerequiredtokeepthewashermovinginacircleunderagivenset

ofconditions.

62

Figure13-1Apparatusforexploringcentripetalforce.CourtesyPASCO.

–Oneway is tohangaknownweight from thestring, Figure13-1 shows this approach.The force is theweight (in

newtons)whichisdeterminedbymultiplyingthemass(inkg)bygravitationalacceleration(9.8m/s2).Thistechniqueis

simpleenough,butitrequiresacertaindegreeofskilltokeeptheradiusfixedforagivenmeasurement.

–Theotherapproachistomeasuretheforcedirectlyusingaspringscale,asindicatedinFigure13-2.Inthiscase,you

needtocoordinateyourmovements,sotheforcestaysnearlyconstantforagivenmeasurement.(Note:Holdingthe

stringatanangleslightlyoff verticalcan introduce justenough friction tostabilize the readingwhile introducingan

errorofonlyafewpercent.)

3.Holdingthetubeinonehand,swingtherubberstopperinasmooth,horizontalcircle.

63

Figure13-2Usingaspringscaletomeasurecentripetalacceleration.

4.Measurehowmanysecondsittakestomaketenrotations,andthendividebytentogettheperiodforonerotation.

Becarefultocountthefirstrotationattheend,ratherthanatthebeginning,oftherotation.Itmayhelptocount“zero”

whenyoustart,andthentocount“one”whenthefirstrotationiscompleted.

5.Usingthemarker,placeaseriesofmarksat1centimeterintervals,startingattheloopforthehangingmass.

6.Usingthemeterstick, identifythedistancebetweenthetopofthetubeandtherubberstopperassociatedwiththe

markclosesttothehangingweight.Youcannoweasilymeasuretheradiusbysubtracting1centimeterforeverymark

belowthetubethatyoucancount.(Youcanalsodeterminetheradiusbymeasuringthelengthofstringbelowthetube

andsubtracting from the total lengthof thestring.) Youcanalsouseapieceof tapeorapaperclip tomark the

positionof thestring togivea radius thatyoumeasurebeforespinning.Howeveryoudo it,makesure thatnothing

restrictsthefreemovementofthestringthroughthetube.

Firstinvestigation:Forceversusvelocity(forfixedradiusandfixedrotatingmass)

1. Setthespringbalancetozero.(It’spreferablethatthespringbalancereadsdirectlyinnewtons.Ifitreadsingrams,

multiplyby0.0098toconverttonewtons.)

2. Attachthebottomofthespringbalancetoaclamponthetableandtheotherendtothestringcomingfromthe

64

tube.SeethepreviousFigure13-2.

3. Starttherubberstoppergoinginacircle.

4. Measure the radius from thecenterof thecircle to the rubberstopper (inmeters).Thisshould remainnearly the

sameforallthesemeasurements.

5. Measuretheperiodorthenumberofsecondsittakestogotencompleterotations.

6. Calculatethevelocity(inmeterspersecond)byusingv=2πr/T,whereristheradius(inmeters)andTistheperiod(inseconds).

7. Measuretheforceonthespringscalewhilethewasherisspinning.Ifyouareusingamasshangingfromthestring,

theforce(innewtons)isequaltotheweightofthemass(massinkgtimes9.8ormassingtimes0.098).

8. Increaseordecreasethevelocitywhilemaintainingafixedradius.Foreachnewvelocity,measuretheforceonthe

spring scale. Repeat for several velocity and forcemeasurementsat (nearly) the same radius, and then plot the

results.

Radiusforalltrials=____meters

Secondinvestigation:Forceversustherotatingobject’smass(forfixedradiusandfixedperiod)

1. Withthespringbalancesettozeroandattachedtothetableasdonepreviously,starttherubberstopperspinningat

amedium-pacedperiod.

2. Measuretheforceandrecordthemassoftherubberstopper.

3. Tieasecondstopper(todoublethemass)attheendofthestring.

4. Repeatbyaddingathirdandthenafourthrubberstopper.

5. Completethedatatable,plotyour results,anddescribetherelationshipbetweenforceandmassfor fixedradius

andperiodfromyourdata.

Radiusforalltrials=(constant)____meters

Periodforalltrials=(constant)____seconds

Thirdinvestigation:Forceversusorbitalradius(forfixedperiodandfixedrotatingmass)

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Thispartismorecomplicatedthantheprevioustwoinvestigationsandwillrequireagreaterdegreeofskillandpatience.

1. Zerothespringbalanceandclamptothetable,asdonepreviously.

2. Starttherubberstoppergoinginacircle.

3. Measuretheradius,measuretheforceonthespringscale,andthenmeasuretheperiodaspreviouslydescribed.

(Throughout thispartof theexperiment, thevelocityneeds tostayasconstantaspossible,so theonlyvariables

being studied are forceand radius.Measure the period and from that determine the velocity. As the radius gets

larger, it will be necessary to allow the period to decrease to maintain a constant velocity. If the velocity is

reasonablyclosetothefirstreading,recordtheradiusandtheforce,aswellasthespringscale.Otherwise,adjust

therateofturningandtryagainuntilthevelocityisreasonablyclose.)

4. Adjusttheradius(eitherlongerorshorter)whilecontinuingtoturnatthesamerate.Foreachnewradius,measure

theforceonthespringscale.

5. Repeatforseveralradiusandforcemeasurementsat(nearly)thesameperiod.

6. Completethefollowingdatatableandplottheresults.

Periodforalltrials=____seconds

ExpectedResults

Thisprojectleadstothefollowingconclusions:

1.The faster the rotation (or theshorter theperiodof rotation), thegreater thecentripetal forceneeded tomaintain

circularmotion.

Fora12-gramrubberstopper,theexpectedresultsareshowninFigure13-3.Thisshowstherelationshipisnot linear,

butthatitincreasesmorerapidlyasthevelocityincreases.

2.Thegreaterthemass,thegreatertheforceneededtokeeptherubberstoppergoingatagivenspeedataparticular

radius.Thisresultisexpectedtobelinear.

3.Foragivenrotationalspeed,theshorterthestring,thegreatertheforceneeded.

For a 12-gram rubber stopper, the expected results are shown in Figure 13-4, which shows an inverse relationship

betweenforceandstringlength.

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Figure13-3Centripetalforceversusvelocity.

Figure13-4Forceversusstringlength.

WhyItWorks

The“string”thatkeepsanobjectgoingaroundinacircleisprovidedbyacentripetalforce.Inthiscase,itisliterallyastring.

Inthecaseofasatelliteorplanet,the“string”isthegravitationalforce.

Thefastertheobjectgoes(foragivenradius),thegreatertheforce,accordingtotheequation:

whereFc is thecentripetal force,m is themassof the spinning object (thewasher in our case), v is the velocity of the

washer,andristheradiusofthecircle.

OtherThingstoTry

Findingthemathematicalmodel

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GiventhedatashowninFigure13-3,wecandeterminethatforceincreaseswiththesquareoftherubberstopper’svelocity

inoneoftwoways:

1.Useacurve-fittingprogram,suchasExcel.Fromascatterplot,withthedataselected,gototheChartmenu,select

AddTrendline,andthenselectapowerfitoption.SelectAddEquationtotheChartfromtheOptionstab.Thisdisplays

themathematicalmodelforyourdata.Theexpectedresultisforthistobetheformy=x2orclosetoit.

Figure13-5Centripetalforceversusvelocitysquared.

2.EitherusingExcelorplottingbyhandmakesagraphofforceversusvelocitysquared.Iftherelationshipisoftheform

expected,thatgraphshouldbeastraightline.ThisisshowninFigure13-5.

Given the data previously shown in Figure13-4, we can determine that force varies inversely with the radius (string

length)usingthesametechniques.

1.HaveExceldeterminethetrendlinefortheexpecteddata,asshownonthegraphforthepreviousFigure13-4.

2.Plottingforceversusthereciprocalofradius(1/r)resultsinastraightline,asshowninFigure13-6.

Figure13-6Centripetalforceversusreciprocalofradius.

Sourcesoferror

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Thisprojectworksreasonablywellandenablesyoutofindthemodelforcentripetalforceusingverysimpleequipment.The

followingarepotentialsourcesoferrorsthatmayimpactyourresults:

1. Frictionbetweenthestingandthetubeoverstatestherequiredforce.

2. Airresistanceresultsinaslightlyslowervalueofvelocity.

3. Atslowerspeeds,thecirclemaynotbeperfectlyhorizontalandmayhaveacomplicatingeffectfromgravity.

Determiningtheaccuracyofthemodelyoufound

Foranyofthepointsyoumeasured,comparetheforceyoumeasured(byeitherthespringscaleorthehangingmass)with

theexpectedvalueforthecentripetalforcegivenby:

ThePoint

Centripetalforcekeepsanobjectrotatinginacircle.Thecentripetalforceequalsthemassoftheobjecttimesthevelocity

squareddividedbytheradius.

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Project14

Agravitywell.Followingacurvedpathinspace.

TheIdea

Inthisproject,youbuildasimplemodelofaplanetgoingaroundthesun.Thismodelexhibitsmanyofthephysicalproperties

foundthroughoutthesolarsystem.YoucandiscoverforyourselfthebasicprinciplesofplanetarymotionasdidCopernicus

andKepler,exceptyouwon’thavetospendyearssquintingthroughatelescopeoncoldwinternights inthemiddleofthe

nighttodothis.Thismodelalsoprovidesan intuitivewaytovisualizeEinstein’stheorythatgravity istheresultofamass

curvingspace.

WhatYouNeed

bucketorothercircularframe

sheetofLatex,largeenoughtocovertheopeningofthebucket

mass(roughly50g)—a1-inchdiametersphericalsteelballwouldbeidealbecauseitcanpositionitselfinthecenter

ofthesheet

marbles,smallsteelballs

Method

1. StretchtheLatexonthebucket.Removethewrinkles.

2. Rollthemarbleacrossthesheetandobservethepathittakes.

3. Now,placethemassinthecenterofthesheet.Thisshouldcausethesheettobecomenoticeablydistorted.Ifthis

isnot thecase, itmaybenecessary to increasethemass,butavoid tearing thesheet.Thecentralmassshould

maintainafixedposition,whichcanbefacilitated,ifnecessary,byalittletape.

4. Rollamarbleinacircularpatharoundthecentralmass.

5. Observethemotionofthemarble.SeeFigure14-1.

6. Observewhathappensifthemarbleisrolledfasterorslowerinagivenpath.Whathappensifthemarbleiscloser

orfartherfromthecentralmass?

ExpectedResults

Thekeyobservationisthatthepathfollowedbythemarbleisanellipse.Thepathmayappearcircular,butellipticalpaths

arecertainlypossible.ThisiscomparabletooneofKepler’sobservationsconcerningplanetarymotion.

Kepleralsoobservedthatthecloseraplanetgetstothesun,thefasteritgoes.Themarblesinthisexperimentexhibitthe

sameproperty.

Ifthemarbleisgivenavelocitythatistoohigh,itwillnotfollowthetypeofellipticalorbitfollowedbytheplanetsaround

thesunbut,rather,theopenhyperbolicorbitfollowedbymeteors.

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Figure14-1

WhyItWorks

Kepler’s law can be derived by equating the centripetal force that keeps a planet in orbit to the gravitational attraction

betweentheplanetandthesun.Thedepressioncreatedbythecentralmassexertsaforceonthecirculatingmarblethat

varieswith position. Although this force does not exactly decreasewith the inverse square of the distance, as does the

gravitationalattractionbetweenaplanetandthesun,itdoesprovideagoodapproximation.

OtherThingstoTry

ThisexperimentalsoprovidesananalogyforunderstandinganaspectofEinstein’stheoryofgeneralrelativity.Theideais

thatwhatwecallgravityisreallyadistortioninspacecausedbythepresenceofamass.Thedistortionofthesheetcanbe

thoughttorepresentthedistortioninspace,whichguidesthepathofaplanetgoingaroundthesun.Asfar-fetchedasthis

mayseematfirst, lightfromstarsemergingfrombehindthesunhasbeenobservedbyastronomerstofollowabentpath

causedbythesun’smass,confirmingEinstein’sprediction.

ThePoint

Objectsinmotionaroundacentralmassfollowanellipticalpath.Theclosertheygettothecentralmass,thefastertheygo.

Gravitationalattractioncanbethoughtofasadistortionofspacecausedbythepresenceofthemass.

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Project15

Howfastcanyougoaroundacurve?Centripetalforceandfriction.

TheIdea

Whatdetermineshowfastacarcansafelygoaroundacurveandnotskidontheroad?Thisprojectexploresturningand

friction,andhowthetwoarerelated.

WhatYouNeed

board (approximately) 36 inches by 4 inches by¾ inch (Other shapes, including a circularly shaped board or a

turntable,canalsobeused.)

verticalpole,suchasaringstand,toserveasapivotpoint

afewcloselymatchedtoycars,suchasMatchboxcars

Figure15-1Positionofcarsbeforerotation.

Method

1. Drillaholeinthecenteroftheboard.Theholeshouldbelargeenoughtoallowtheboardtofreelyrotateonthe

post.

2. Placeeachofthecarsalongalinerunningfromthecentertotheouteredgeoftheboardatapproximately6-inch

intervals,asshowninFigure15-1.(Youcanalsodothiswithpenniesorotherobjectsinsteadofcars.)

3. Predictwhatyouthinkwillhappentothecarsasyoustarttorotatetheboardaroundthepivotpoint.

4. Rotatetheboard,veryslowlyasfirst,butthenpickupspeed.Whathappenstothecars?

ExpectedResults

Carsfurthestfromthecenterbegintomovefirst.Asthecarsstarttomove,theymoveawayfromthecenter,asshownin

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Figure15-2.

WhyItWorks

Thecarsremainontheboardaslongasthefrictionalforceisgreaterthanthecentripetalforceneededtokeepthecars

movinginacircularpath.Thefurtheryouarefromthecenterofrotation,morecentripetalforceisneeded.Forthisreason,

thecarsfurthestfromthecenterarethefirsttomove.

Figure15-2Carsfurtherawayfromthecenterofrotationrequiremorefrictiontoremainstationary.

OtherThingstoTry

Thiscanalsobedoneusingpenniesonarotatingsurface,suchasaturntable.

ThePoint

Frictioncanprovidethecentripetalforceneededtokeepanobjectmovingalongacircularpath.Iftheforceoffrictionisnot

sufficienttoprovidethecentripetalforceforagivenradius,theobjectwilldepartfromitscircularpath.

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Project16

Ping-pongballsracinginabeaker.Centripetalforce.

TheIdea

Inthisproject,yougetapairofping-pongballscirculatingrapidlyinabeakerwithablowdryer.Theballscontinueracingina

frantic high-speed circular path long after the blow dryer is removed. This is a fun, attention-getting demonstration that

exploresvariousaspectsofcircularmotion,includingangularvelocity,centripetalforce,andtheeffectoffriction.

WhatYouNeed

250mLglassbeakerorplasticcontainerroughly5inches(12cm)indiameter

2ping-pongballs

blowdryer

Method

1.Placetheping-pongballsinthebeaker.

2.Withonehand,holdthebottomofthebeaker.Theotherhandholdstheblowdryer.(Noheatisneeded.)

Figure16-1PhotobyS.Grabowski.

3.Directtheairfromtheblowdryertorapidlycirculatetheairflowinacircularhorizontalpatterninsidethebeaker.

Figure16-2PhotobyS.Grabowski.

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4.Theblowdryershouldgettheping-pongballstorapidlyspininsidetheglasscontainer.

Figure16-3PhotobyS.Grabowski.

5.Assoonastheping-pongballsarespinningrapidly,quicklyturnthebeakerupsidedownand(carefully)placeitonthe

table.

Figure16-4PhotobyS.Grabowski.

ExpectedResults

Theping-pongballscontinuetorevolvearoundtheinnerwallsofthecontainer.Whilespinning,theyappeartodefygravity.

Theyalsotendtomoveasfarawayfromeachotherastheycan,especiallyastheyslowdown.

WhyItWorks

75

Therapidlymovingairgivestheping-pongballskineticenergy.Theinnerwallsofthebeakerprovidecentripetalforcethat

keepstheballsmoving inacircularpath.Theforcebetweentherotatingballsandthesidewallofthebeakerresults ina

frictional force that is large enough to hold the balls suspended above the table as they rotate. The balls have enough

angularmomentumtokeepgoinguntilfrictionalforcesbetweentheballandthewallsofthecontainercausethemtoslow

down,resultingintheballscontinuingtorotatemoreslowlyanddroptothesurfaceofthetable.

Figure16-5PhotobyS.Grabowski.

The rapid rotationcauses frictionbetween theballsand thesideof thebeaker.Thiscancause thepingpong-balls to

becomecharged,resultingin(minor)attractiontothewallsofthecontainerandrepulsionfromeachother.

OtherThingstoTry

Asimilareffectcanbeachievedbyvigorouslyrotatingapairofmarblesinaninvertedglassorbeaker.

ThePoint

The ping-pong balls are given kinetic energy by the blow dryer. Likeall rotating objects, their inertia tends to keep them

moving inastraight line.The insidewallsofthebeakerapplycentripetalforce,whichcausesthepathtobecircular.The

ballscontinuetomoveuntilthekineticenergyisconvertedintofriction.

76

Project17

Swingingapailofwateroveryourhead.

TheIdea

Ifyoufillabucketwithwaterandturnitupsidedown,thewaterwill(ofcourse)spillout.But,ifyouspinthebucketoveryour

headfastenough,youmayavoidgettingwet.Howfastdoyouhavetoswingapailfilledwithwateroveryourheadsoasto

notgetwet?Inthisproject,youexplorewhatittakesnottogetsoakedor,inotherwords,howfastisfastenough?

WhatYouNeed

smallbucketwithahandleorstringattached

water

stopwatch

meterstick

personwillingtogetwet

anotherpersonwillingtogetthefirstpersonwet

optional:papertowelsoramoptowipeupspills

optional:raincoatorumbrella

Method

1. Putsomewaterinthebucket.

2. Predicthowfastyouthinkyouneedtospinthebuckettoavoidspillingitscontents.Thiscanbedonequalitativelyby

spinning at a relatively fast rotation and pushing your luck by going progressively slower.One simple refinement

would be to do this in terms of time (in seconds). Amore quantitative prediction can be based on the linear or

angularvelocity,anditcanbemeasuredbasedontheperson’sarmlength.)

3. Spinthebucket,asshowninFigure17-1,andevaluateintermsofthepredictions.

ExpectedResults

Theslower yougo, thegreater the riskof soaking thespinner foragiven radius. If yourarm is shorter, youwill have to

completethecircleinlesstime.

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Figure17-1Spinningabucketfilledwithwateroveryourhead.

The maximum time to go around a vertical circle of a given radius without spilling is shown in the table below. The

maximumtimetospinthebucketoverheadisabouthalfthattime.Keepinmindthesetimesarebasedonuniformvelocity.

Themostcriticalpointofcourseisatthetopofthecircle.(Ifyouslowdownthere,youmayneedthatraincoatidentifiedin

thewhat-you-needlist.)

WhyItWorks

Thepersonspinningthebucketwillbesparedasoakingaslongasthebucketmovesfastenoughsothecentripetalforceis

greaterthantheforceofgravity.

Theconditionforthisis:

Note,thisresultindicatesitdoesn’tmatterhowmuchwaterisinthebucketaslongasthespinnermovesatasufficient

speed.Thelargertheradius,thefasteryouhavetogo.Toomuchwater,however,maycausethespinnertoslowdown.

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OtherThingstoTry

Thiscanalsobedoneusingconfettiinsteadofwater.

Physicsalert:thereisreallynosuchthingasacentrifugalforce.Thewaterisgivenavelocityandisforcedintoacircular

pathby thecentripetal forceexertedby thebottomof thebucketon thewater. If thebucket ismoving fastenough, the

centripetalforceofthebucketisneededtokeepitgoinginacircle.Ifthebucketisnotgoingfastenough,gravitywouldbe

greatenoughtocausethewatertospillout.

ThePoint

Thecentripetalforceonthewaterisprovidedbythebottomofthebucket.Thehandleofthebucketprovidesacentripetal

forceonthebucketitself.Thewaterwillnotfalliftherateofrotationishighenoughthatthecentripetalforceisatleastas

greatasgravity.

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Section3

Gravity

Project18

Featherandcoin.

TheIdea

Doesanobjectwithagreatermassfallfasterthananobjectwithalowermass?

This isa fundamental issue thatwasaddressedbyGalileo,aswellasApolloastronautson themoon.Afterdoing this

experiment,youcanweighinonthisquestion.

WhatYouNeed

feather

coin

clearcylindricalplastictube

capstofittheendofthetube—oneclosedandonewithavacuumfitting

vacuumpump

Method

1. Putthecoinandthefeatherinthetube.

2. Inserttheendcapsineachoftheendsofthetube.

3. Withbothobjectsonthebottomendcap,invertthetubeandletthefeatherandthecoinfallinthetube.Makesure

bothareabletofallfreelywithoutinterference.

4. Attachthevacuumpumptothetubeandevacuatetheairfrominsidethetube,asshowninFigure18-1.

5. Invertthetubeandobservetheresultsagain.

Figure18-1Clearplastictubeattachedtovacuumpump.

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ExpectedResults

Withairinthetube,thecoinwillfallfaster,asshowninFigure18-2.

Figure18-2Withairpresentinthetube,thecoinfallfaster.

Withairremovedfromthetube,bothobjectsfallatthesamerate,asshowninFigure18-3.

(Twothingscouldresultinanunintendedoutcome,whichshouldbeavoidedifpossible:Withairinthetube,thecoinmight

pushthefeathertowardthebottomatafasterratethanitwouldfallonitsown.Also,someelectrostaticdragmightdevelop

betweenthefeatherandtheplastic,whichslowsthedescentofthefeatherinavacuum.)

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Figure18-3Withairremovedfromthetube,bothobjectsfallatthesamespeed.

WhyItWorks

ThereisnodoubtthatthegravityoftheEarthexertsagreaterforceonamoremassiveobject.However,themoremassive

objectrequirespreciselythatsameamountof largerforcetocauseittoaccelerate.Theupshot isthatallobjectsonthe

surfaceoftheEarthaccelerateatthesameconstantrate.

OtherThingstoTry

Thisexperimenthasanumberofvariations,including:

Comparethedescentofacrumpledsheetofpaperwithanunfoldedsheetofpaper(bothofthesamemass).

Comparethedescentofasinglepencilwithseveralpencilsbundledtogether.

Tieaweight(suchasalargestainlesssteelnut)toastringatthefollowingintervals:125cm,80cm,45cm,20cm,

5cm.Holdthestringvertically.Whendropped,eachweighthitsthefloorinthesametimeinterval.Thisisbecause

thedistanceeachweightfallsisproportionaltothesquareofthetimethatitisfalling.Theseintervalsarebuiltinto

82

thespacingoftheweights,sotheyshouldhitatthesametimeinterval.

Whichfallsfaster(inair):abookoradollarbill?Certainly,ifthey’redroppedsidebyside,thebookwillfallfastest.

However, if the dollar bill is placed on top of the book or below the book, the effect of air resistance will be

eliminatedandtheywillfalltogether.

ThePoint

Gravitationalacceleration(inavacuum)isaconstant.Specifically,itdoesnotdependonthemassofthefallingobject.

83

Project19

Howfastdothingsfall?

TheIdea

Objectsexposedtotheforceofgravityaccelerateatthesamerate.Weprovedthat inthepreviousexperiment.Here,we

measuretherateofgravitationalaccelerationforallobjectsontheearth.

Youmeasureaccelerationtwodifferentwaysinthisexperiment.Inthefirstmethod,youuseastopwatch.Wecallthisa

ballparkexperiment,whichmeansweexpectittogivearoughapproximationratherthanaveryaccurateresult.

Thesecondmethodinvolvestheuseofamotionsensor,whichoffersagreaterdegreeofprecision.

WhatYouNeed

Stopwatchmethod

variousobjects:baseballs,golfballs,bowlingballs,yourphysicstextbook

stopwatch

tapemeasure

Motionsensormethod

motionsensorwithDataStudiosoftware

ringstandorothersupporttoorientthemotionsensorvertically,lookingdownward

basketball,softball

Method

Stopwatchmethod

1. Usethetapemeasuretoidentifythedistancetheobjectwillbedropped.

2. Onepersondropstheobjectandtheotherpersontimesthetripdown.

3. Start the timer just as the object is released and stop it at the precise time it hits the ground. Try to avoid

anticipating the release that will give too large a time measurement and an understated value for gravitational

acceleration.

4. Calculatethegravitationalaccelerationusingtheequationg=2d/t2,wheredisthedistanceinmetersandtisthe

time inseconds.Gravitationalacceleration ismeasured inm/s2,which is readasmetersper secondsquaredor

meterspersecondpersecond.

Motionsensormethod

1.Setupamotiondetectormountedonatablewithanunobstructedviewofthefloor,asshowninFigure19-1.

2. Set up themotion detector to read distance versus time and velocity versus time. This can be accomplished by

selectingthe“velocity”filethatcomeswiththeDataStudiosoftwarepackage.

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Figure19-1Motionsensoralignedtomeasureverticalmotion.CourtesyPASCO.

3. This measurement works best by increasing the frequency of the motion sensor measurement by increasing the

samplingfrom10persecondto50persecond.

4.Alignthemotionsensorintheverticaldirection.

5.Hold theball justunder themotionsensor,asshown inFigure19-2.Start the readingsand release theball.Try to

avoidimpartinganyverticalmomentumtotheballbylettingitdropwithoutaninitialpushordelayedrelease.

6.Capturethemotionoftheballthroughseveralbounces.

7.Measure the slope of the velocity versus time graph. Use either the initial descent or the first bounce. The initial

descenthastheadvantageofhavingthelargeststatisticalsample.Thefirstbouncehastheadvantageofbeingfree

oferrorsassociatedwiththerelease.

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Figure19-2CourtesyPASCO.

ExpectedResults

Foreithermethod,theacceptedvalueforgravitationalaccelerationisabout9.81m/s2.Thismayvaryslightlywithlocation

andelevation.

Stopwatchmethod

Foratypicaloutdoorhigh-schoolathleticbleacherabout15feetabovetheground(about4.6meters),anobjectwill take

about1secondtofall.Welearninthenextprojectthataperson’sreactiontimecaneasilybeasmuchas¼second.Asa

result,anygivenmeasurementmayhaveanerrorofasmuchasabout25percent.(Thiscanbeevengreaterbecausethere

canbenon-offsettingerrorsforthestartandstoptimeofthemeasurement.)Thisisnotveryprecise,butitputsusinthe

ballpark.Itishardtoimproveonthisbecauseofthelimitationinmeasuringtimeinherentintheuseofastopwatch.Some

peoplefindthatlisteningfortheballtohitthegroundiseasiertotimethantryingtoobserveitvisually.Agreaterdistanceto

fallalsoreduceserrorsbecausethereactiontimeisasmallerpercentageoftheoveralltimemeasured.

The following chart summarizes expected times for various distances. Timesmeasured in this range gives reasonable

valuesforgravitationalacceleration,g.

86

Another resultexpected is that,within theaccuracyof thisexperiment,allobjects fallat thesamerateofacceleration,

regardlessoftheirmass.

Noticehowsensitivetheresultsareonthetimemeasurement.Forinstance,supposeyoudropabowlingballfroma4.6

meterheightandmeasure1.1secondsinsteadof1.0seconds.That0.1seconderrorwouldresultinacalculatedvaluefor

gravitationalaccelerationof7.6m/s2insteadoftheexpectedvalueof9.8m/s2ora22percenterror.A0.1seconderroris

lessthanthereactiontimeofmostpeoplesoitisagoodthingthatwehaveanotherwaytomakethismeasurement.

Motionsensormethod

Withamotionsensor,therangeofmeasurementsismuchtighter.ThepositionversustimegraphisshowninFigure19-3.

Notice thisshowsacurved line typicalofacceleration.As theball falls, theposition increases,s theportionof thecurve

sloping up to the right represents the falling motion. After the ball bounces off the floor, the distance increases, which

generatesthecurvedlinethatslopesdowntotheright.Thisgraphshowsaninitialreleaseandthentwobounces.Thedata

collectionstopsjustbeforeathirdbounce.

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Figure19-3Positionversustimeforafallingballshowingtwofullbounces.CourtesyPASCO.

A velocity versus timegraphgeneratedbyamotion sensor is shown inFigure19-4.Gravitational acceleration is given

directlybytheslopeof the line.Thiscanbedeterminedbydividingtherise(change invelocity)by therun (corresponding

changeintime).TheslopecanalsobefoundbyusingtheslopetoollocatedintheDataStudiopull-downmenu.Thisgraph

showsthesamedropfollowedby twobounces,asyousaw inFigure19-3.Noticethefirstbounceoccurs justbefore1.2

seconds.Theballreachesitsfirstpeakat1.5secondsandbeginstofallagain.InFigure19-4,thevelocityrapidlychanges

frompositive(abovetheline)tonegative(belowtheline).

Alsonoticeoneinterestingaspectofthephysicsoffree-fall,illustratedbyFigure19-4.Aftereachbounce,theslopeisthe

samebelowthezero line(bouncingup),atthezero line(atthehighestpoint)andabovethezero line(fallingbackdown).

Whatthismeansisgravitationalaccelerationisconstantandaffectsanobjectinfree-fall,regardlessofwhetheritismoving

upordown.

Figure19-4Velocity versus time for a falling ball. The slope of each line gives the acceleration of the ball in free fall.

CourtesyPASCO.

WhyItWorks

Part1isadirectmeasurementandapplicationofthebasicmotionformula:

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a=2d/t2

wherewefindtheaccelerationduetotheforceofgravity.

Part2measuresthesamething,butitusesamuchmoreprecisemeasurementofthedistancetraveledinagiventime.

WeknowfromProjects1and2thattheslopeofthedistanceversusthetimegraphgivesameasureofvelocity.Similarly,

theslopeofthevelocityversusthetimegraphgivesacceleration.Eachbounceprovidesareplicationofthisexperimentthat

canprovideaseparatedatapoint.

OtherThingstoTry

Amotionsensorrevealsthebrief timethataballencountersthegroundas itcompresses,decompresses,andeventually

reversesdirection.Someballsdothismorequicklythanothers.Thiscanbeseenintime-lapsephotographybutcanalsobe

noticeableinthedistanceversustimegraphsgeneratedbymotionsensor.

ThereisanothermethodformeasuringtheEarth’sgravitationalaccelerationusingapendulum.SeeProject22.Compare

thiswiththeresultsyougetwiththemotionsensor.

ThePoint

ThisexperimentgivestwowaystomeasuretheaccelerationonanyobjectcausedbythegravitationalforceoftheEarth.

Thefirstwayisadirectmeasurementlimitedbythereactiontimetorecordhowlongittakesanobjecttofall.Thesecond

methodusesamotionsensorthatcapturesthisdatawithgreaterresolutionandprecision,andwheninterpretedgraphically

givesamoreaccuratevalueforgravitationalacceleration.Ineithercase,thecorrectvalueis9.8m/s2or32ft/s2.

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Project20

Thebuckstopshere(thefallingdollar).Usingametersticktomeasuretime.

TheIdea

Thisexperimentexplores thenatureof free-fall: the longeranobject falls, thegreater thedistance it falls.Measuring the

distanceanobjectfallscangiveanindicationofthetime.Thiscanbeusedtoestimateaperson’sreactiontime.Youuse

bothadollarbillandametersticktoprovethispoint.

WhatYouNeed

meterstick

Method

1. Thisrequirestwopeople.Thefirstpersonholdsameterstickupsidedown,sotheendthatreads0cmisdirected

downward.

2. Thesecondpersonholds their fingersat thebottomof themeterstick ready tograb themeterstick,asshown in

Figure20-1.

3. Themeterstickisdropped,andthencaughtasshowninFigure20-2.

4. Thedistance themeterstick falls is an indication of the person’s reaction time. Under gravitational acceleration,

distanceisrelatedtotimeaccordingtotheequationd=½gt2whereg isthegravitationalaccelerationconstant,

9.8m/s2,andtimeismeasuredinseconds.Thisequationgivesthedistanceinmeters.Thisrelationshipistabulated

inTable20-1:

Figure20-1Readytocatchthemeterstick.

90

Figure20-2Thepositionwherethemeterstickiscaughtisanindicationofthetimeitwasfalling.

Table20-1

ExpectedResults

The reaction time can be determined by the distance that themeterstick falls before being caught. Themeterstick will

typicallyfallabout10–20centimetersbeforebeingcaught,butthiswillvarywiththeindividual.

WhyItWorks

91

Thedistanceanobjectfallsincreaseswiththesquareofthetimeitfalls.Similarly,thetimeittakestofallisproportionalto

thesquarerootofthedistance.

OtherThingstoTry

Adollarbillisabout15.2cm(6inches)inlength.Accordingtothepreviouschart,itwilltakeadollarbillnearly0.18seconds

tofall.Challengesomeonetocatchthedollar.Unlessthepersonanticipatesthatrelease,thebillwillfall(almosteverytime).

Figure20-3Moneyoftenseemstofall throughourhands. Itfallsthroughitsownlength inatimelessthanmostpeople’s

reactiontime.

Typical human reaction time is about ¼ second. Most of the time, people are unable to catch the bill. Occasionally,

someonecangetluckyandanticipatethefallingdollar.Ifyouareofferingtoletthepersonkeepthebilliftheycatchit,you

maywanttoconsiderasmallerdenomination.

ThePoint

Thedistanceanobjecttakestofallisrelatedtothetimeittakestofallthatdistance.Knowingthetimeletsyoupredictthe

distance.Similarly,knowingthedistanceletsyoupredictthetime.

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Project21

Weightlesswater.Losingweightinanelevator.

TheIdea

Whenthingsfall,theynolongerseemtohaveweight.Objects,includingpeople,floatintheSpaceShuttleasiftherewereno

gravity.Theshuttleorbitisnotthathighabovetheearth’ssurfaceforthegravitationalattractiontotheEarthtodisappear

and,iftheshuttlewerenotmovingsorapidlyinorbit,itwouldbepulledstraightdowntotheearth.So,wheredoestheforce

of gravity go to make the shuttle astronauts seem weightless? It has to do with the forces on falling objects. In this

experiment,youinvestigatewhathappenstotheweightoffallingobjectsusingafallingcupofwaterandbyholdingaweight

onascaleinanelevator.

WhatYouNeed

cupwithafewholesinit

water

springscale

mass

optional:anelevator

Method

Cup

1. Fillthecupwithwater.Observewhathappens.

2. Dropthecup(overasinkorbucket).Observewhathappens.

Elevator

1. Hangthemassonthespringscale.

2. Withthemassheldstationary,notetheweightoftheobject.

3. Whileholdingthescale,letthescaleandmassdroptowardthefloor.Stopbothjustbeforetheyhitthefloor.

4. Youdon’thavemuchtimetodothis,butobservethescalereadingasitfirststartstofallandthereadingasitis

slowedpriortohittingthefloor.

5. Again,whileholdingthescale,raisethescaleandmassfromthefloor.Bringittoastopwhileyou’restillholdingit.

6. Ifyoucangettoarealelevator,observethescalereadingwiththemasssuspendedastheelevatorgoesupandas

the elevator goes down. Even in a real elevator, you will find the period of acceleration for you tomake these

observationsisshortbecauseelevatorsreachasteadyvelocityfairlyquickly.

ExpectedResults

Thewaterdripsoutfromtheholeswhenthecupisfilledwithwaterandheldstationary.Thewaterstopsdrippingwhenthe

cupisinfree-fall.

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Thescalereadsagreaterweightwhenyouliftthemass.Withyourarmfullyextendedasthescaleandmassslows,the

scalereadsalowerreadingthanwhilestationary.

Thescalereadsalowerweightwhenyoudropthemass.Asyouslowthescaleandmassasitnearsthefloor,thescale

readsahigherreadingthanwhilestationary.

Withtheelevator,thescalereadsahigherweightwhenitfirststartstogoupandalowerweightastheelevatorslowsto

thenextstop.Goingdown,thescalereadsloweratfirst,andthenhigheratthenextstop.

If the starting-up and slowing-down phase is uniformly spread over about 1 second, the change in apparent weight

measuredbythescaleshouldchange(verybriefly)bynotquite50percent.Thesechangesare illustrated inthefollowing

Figures21-1,21-2,and21-3.

Figure21-1Objectatrest.

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Figure21-2Upwardacceleration.

Figure21-3Downwardacceleration.

WhyItWorks

With thecupheld, thewater isdrawnthroughtheopeningsbygravity.However,whenthecup is in free-fall, it fallsat the

samerateas thewater.While falling, thewater is (apparently) “weightless,”similar toastronauts in theshuttle. If thecup

wasn’t falling, thebottomof thecupwould resist thatpull, leaving thewaternoother resort than to falloutof theholes.

However, with the cup falling, the water does not experience a force from the cup opposing its downward movement.

Becausethecupwasfalling,thewaterinthecupseemedweightless.

Wehaveallseenimagesofastronautsfloatingintheshuttleandspacestation,asiftheywere“weightless.”Asatubeof

scrambledeggsfloatsbyanastronaut, itcertainlyappearsthatway.However,weight is theforcecausedbygravityona

massand,althoughthatattractiondropsoffastheinversesquarerootofthedistance,itneverbecomeszero.Infact,atthe

shuttleorbitof200km,theforceoftheEarth’sgravitationalattractionisonlyabout6percentlowerthanwhatitisonthe

surfaceoftheearth.

Objects inorbitareessentially fallingataspeedconsistentwithmaintaining theorbit.Theapparentweightlessnessof

objectsinspaceistheresultoftheobjectsintheshuttlefallingtoEarthatthesamespeedastheshuttleitself isfalling.

Becausethewaterisfallingatthesamespeedasourcup,it,too,appearsweightless.Whenweholdthecup,webalance

theforceofgravityonthecuponly,butnotonthewater.Inthatcase,thewaterhasweightthatspillsoutoftheholesinthe

95

cup.

The weight measured on the scale is a combination of the actual weight decreased or increased by the effect of

accelerating theweight. It does notmatter how fast theweight ismoving.Once a high-speed elevator gets going at its

cruisingvelocity,themeasuredweightshouldexactlyequalthestationaryweight.Itisonlytheaccelerationexperienceduring

thestoppingandstartingthataffecttheforceontheobjectduringthattime.

OtherThingstoTry

Avisualaccelerometercanbeusedtoindicatethedirectionandrelativemagnitudeoftheaccelerationsthataccompanythe

weightchangesencounteredhere.

Figure21-4CourtesyPASCO.

Usingamotionsensortomeasureanobjectmovingupandthendownaninclineprovidesacloserlookattheacceleration

ofanobjectsubjectedtogravity.Figure21-4showstheaccelerationversustimedisplayedinDataStudio.Thisshowsthat

accelerationisdownward(slightlymorethan−2m/s2)forboththeuphillanddownhillsegmentsofthegraph.

ThePoint

Thesensationofweight iscausedbyaforce(suchastheground)holdingyouup.Thisupward(ornormal)force,whether

exerted from below (as in the cup) or above (as with the scale and weight), is howwe experienceweight. If the object

supportingusisalsofalling,wearenolongerexposedtotheforceweexperienceasweight.

96

Project22

Whatplanetareweon?Usingaswingingobjecttodeterminethegravitational

acceleration.

TheIdea

ThisprojectexploresanindirectwayofmeasuringthegravitationalaccelerationoftheEarth(oranyotherplanetyoumaydo

thisexperimenton).Becausegravitationalaccelerationaffectshowfastapendulumswings,wecantakeadvantageofthat

tofindthegravitationalaccelerationprovidedbymeasuringtwothings:howlongthependulumisandhowmuchtimeittakes

toswingbackand forth. (If youare less thaneighteenyearsold,pleasebesure toget yourparents’permission forany

interplanetarytravelforthisproject.)

WhatYouNeed

pendulumconsistingofamasssupportedbyastringattachedtoasupport

pendulumwithalongstringandalargemasssuchasabowlingballsupported(safelyandsecurely!)fromtheceiling

stopwatch

Method

1. Measuretheperiodofapendulumbymeasuringhowlongittakesforthependulummasstoswingbackandforth

onetime.Sincethismaybelessthanasecond,moreaccuratemeasurementscanbemadebycountingthetimefor

10back-and-forthexcursion,andthendividingby10.Rememberthatincountingthecycles,thefirstcycleiscounted

whenthemassreturnstothepointfromwhichitwasreleasedandnotatthepointwhenitisfirstreleased.

2. Measurethelengthofthependulum.Thisisthedistanceinmetersfromthecenterofthehangingmasstothepoint

ofattachment.

3. Try to minimize vibration of the ring stand or other support structure. Also keep the pendulum moving in two

dimensions.Somepeopleliketouseadoublestring—oneoneithersideofthemass—tokeepthependulumfrom

wobbling.

4. Calculatethegravitationalacceleration,g(inmeterspersecondpersecond),usingtheequation:

whereLisstringlengthinmetersandTistimeinseconds.(ThiswillalsoworkifyoumeasureLinfeetbutyouwillget

ananswerinfeetpersecondpersecond.)Trythismultipletimesandtaketheaveragetogetthemostaccurateresult.

SeeFigure22-1.

ExpectedResults

Gravitationalaccelerationshouldbeclose to theacceptedvalueof9.81m/s2.Resultswithin2percentof this valueare

easilyachievable. Ifyouareworkingwithfeet,gravitationalacceleration is32feet/s2.Longerpendulumlengthsencounter

lessfrictionallossandareeasiertogetanaccurateperiodmeasurement.Remember,100centimetersisequalto1meter

whendeterminingthelengthofthependulum.

97

Figure22-1Usingapendulumtofindg.

Thefollowingsetofvaluesresultsinthe9.81m/s2targetvalueforgravitationalacceleration:

WhyItWorks

98

Itstands to reason that thegreater thepullofgravity, thefaster thependulummotionand theshorter theperiod.This is

givenbytheequationfortheperiodofapendulum:

whereL is the length (in meters) and the period is one cycle back and forth (in seconds). Solving this for gravitational

accelerationgivesus:

Thedefinitionoftheperiodofapendulumisthenumberofsecondsforittoswingbackandforthonetime.

OtherThingstoTry

Youhavebeencapturedbyalienabductorsandtakentoanunknownplanet(wheretherearenovideogamesandnocable

TV).Youareabletoremoveyourshoe,whichhasa15cm(0.15m)shoelace.Youfindthatwhenyouletyourshoeswing

freelyinashortarc,itreturnstothepointfromwhichitwasreleasedin1.26seconds.Towhichplanetshouldyoudirectthe

interplanetaryrescueteam?Thegravitationalaccelerationonthevariousplanetsis:Venus8.93m/s2,Earth9.81m/s2,Mars

3.73m/s2, Jupiter924.9m/s2,andSaturn10.6m/s2. Try it. (Hint: theanswer is this planet is oneofEarth’s neighbors in

spacepossessingaverythinatmosphere,icecaps,andareddishclay-likesurface.)

ThePoint

For a given string length, the period of the pendulum depends on the gravitational acceleration. This provides a fairly

accuratemethodformeasuringthelocalgravitationalacceleration.

99

Section4

ForceandNewton’sLaw

Project23

Newton’sfirstlaw.WhattodoifyouspillgravyonthetableclothatThanksgivingdinner.

TheIdea

Anobjectatrest(includinganobjectatrestontopofatablecloth)tendstostayatrestunlessactedonbyanexternalforce.

Onewaytoprovethisistopullaclothoutfromundertheobject.Thiscanbedonemoresimplyatfirstormoreelaborately

asyoubuildyourconfidenceinthelawofphysics.

WhatYouNeed

tablecloth (one with low friction is best—tweedy fabrics, gravy spots, and spilled soda can increase friction and

compromisetheintendedresults)

table

objectstoplaceonthetableclothsuchasbowls,bottles,litcandles,andyourphysicstextbook

spareroastturkey,stuffing,andcranberrysauce,ifyouactuallyattempttodothisatyourThanksgivingdinner

Method

1.Placetheclothonthetable,soatleastseveralinchesextendbeyondtheedgeofthetable.

2.Carefullyplacetheobjectsonthecloth.Iftheobjectsareclosertotheedgeofthetablethisiseasier,butallowforat

leastafewinchesfortheobjectstoslide.

Figure23-1Don’thesitate!

3.Atthispoint,allyouneedtodoispullthetableclothoutfromundertheobjectsonthetable.Aswithaband-aid,the

fasterthebetter.Don’thesitateandbetentativewithyourpullbecausethatincreasesthechancesfortheobjectsto

topple.(Itdoesn’thurttocreatesuspensebypretendingyouneverdidthisbeforeandhaveeveryreasontoexpectit

tofail.Themoreyoudothis,thegreaterlevelofactingskillsthismayrequire.)

100

Figure23-2Afastpullworksbetterthanatentativepull.

4.Youcanalsodothiswithjustonebeakerandacloth.Perhapsthisisaless-dramaticstart,butitstillprovesthesame

point.

Note:Thisworksbestwhenobjectsplacedonthetableclothhavesmoothbottomsurfaces.Bowlswithacircularliptendto

catchonthetablecloth.Potterywithafeltbottomormountedsiliconrubberrestingpointscanalsoleadtohumiliationand

ridiculeiftheyhangupduringthisdemonstration.Theobjectsshouldhaveashortvertical“momentarm,”whichmeansbowls

are safer than bottles and partially filled bottles are safer than empty bottles. Bottles with liquid should be at room

temperaturetoavoidcondensationontheoutsideofthebottle,whichcanincreasefriction.

ExpectedResults

Theclothisremovedandtheobjects-at-restsittingonthetableclothtendtostayatrestinapproximatelythesameposition

theywereoriginallyplaced.Mostlikely,therewillbesomeslidingandeventeeteringbeforetheobjectscometorest.

Thecriterion forstability is that theheight todiameter ratio forcylindricalobjectsbe less than thecoefficientofstatic

frictionbetweentheclothandtheobject.

WhyItWorks

Thisisbasicallyafunexperiment,butthereisagoodbitofphysicstolearnhere.Theobjectsretaintheirpositionsonthe

table due to Newton’s first law, which states that an object in motion tends to stay in motion unless acted upon by an

externalforce. (Anobjectat rest tendstostayat restunlessacteduponbyanexternalforce.) Ifexcessivefrictionexists

betweentheclothandthebottomoftheobjects,therewillbeanexternalforceandtheobjectswillmove.Thetablemust

havelowenoughfrictionsothetableclothcanbepulledoutsmoothly,butenoughfrictionsotheobjectsdon’tslidetoofar

aftertheclothisremoved.Thesmallfrictionalforcethatoccurswhentheclothispulledoutexertsatorquethatcanrotate

theobject,especiallyonewhosecenterofmassisrelativelyhighabovethetable.Thefrictionalforceexertedbythetableon

the bottom surface of the objects opposes this rotational motion and helps stabilize tall objects, such as bottles and

candlesticks.

OtherThingstoTry

Asaway toget in touchwith your inner nerd, youcandrawdiagrams, called free-body-diagrams, showingall the forces

101

presentinthisproject.Youcanlearnalotofphysicsbydoingthis.

ThePoint

OneaspectofNewton’sfirst lawisthatanobjectatresttendstostayatrest.Thiscanbeseeninthereluctanceofthe

objectsonthetabletobemovedastheclothispulledoutfromunderthem.Somefrictionalforceexistsbetweenthecloth

andtheobjects,whichexertsatorquethat,ifstrongenough,willrotateandtoppletheobject.

102

Project24

Newton’sfirstlaw.Pokerchips,weightonastring,andafrictionlesspuck.

TheIdea

ThisexperimentfurtherexploresNewton’sfirstlawinboththehorizontalandverticaldirections.

WhatYouNeed

5to10pokerchips(orcoins)

table

string—strongenoughtosupportthemass,butweakenoughtobreakwhenpulled

1weightwithattachmentpointsonboththetopandbottom

1supporttohangtheweight

Method

Chips

1. Placethechipsinaverticalstackonthetable.

2. Thetableshouldbesmoothenoughforthechipstoslidefreelyacrossitssurface.

3. Takeonechipanddirectittowardthestackbyflickingitwithyourfingersorpushingitrapidlytowardthestack.

Weightonastring

1. Youaregoingtodothistwice(twodifferentways),soifyouhaveenoughmaterials,itworksbestifyouduplicatethe

set-upside-by-side.

2. Usethestringtohangtheweightfromthesupport.

3. Attachastringonthebottomoftheweight.

4. Predictwhatwillhappenwhenyoupullthestring.

5. Firsttime—pullthestringslowly.

6. Secondtime—pullthestringquickly.

ExpectedResults

Theslidingchipshouldknockoutthebottomchipandtakeitsplaceinthestack(Figure24-1).

103

Figure24-1Inertiakeepstheupperchipsinplacewhiletheloweroneisremoved.

Figure24-2Wherethestringbreaksdependsuponhowfastyoupull.

Pullingthestringslowlycausesonlytheupperstringtobreak.

Pullingthestringquicklycausesonlythebottomstringtobreak.

WhyItWorks

ThesearesimpledemonstrationsofNewton’sfirst law.Thestackofpokerchipsremainsarerest.Themomentumofthe

movingchipistransferredtothechipitreplaces.MomentumisexploredinSection5inthisbook.

When the string is pulled slowly, the force from pulling is added to the weight pulling down on the upper string. The

combinedtensionisgreaterontheupperstringandthatisthestringthatbreaks.

Whenthebottomstringispulledrapidly,themass,whichisatrest,tendstostayatrestandthetensionisappliedtothe

bottomstring,whichbreaks.

OtherThingstoTry

YoucanexploreNewton’sfirstlawinanumberofotherways.Theseinclude:

1.Cutorteararectangularsheetofpapernearlyinthirds,leavingjustashort⅛inch(1mm)pieceofpaperremainingtoholdthesectionstogether.Challengesomeonetopullsidewaysatbothends(perpendiculartothetears)tocausethe

centersectiontodrop.BecauseofNewton’sfirstlaw,thisisvirtuallyimpossible.

104

Figure24-3Itisjustaboutimpossibletomakethecenterpieceofpaperfallbypullingtheothertwopiecessideways.

2.Placeahandfulofcoinsonyourinnerarmwhileit’sbent.Inonequickmotion,swingyourarmforwardandcatchthe

coinsinmidair.Inthefirstone-tenthofasecond,thecoinsfallonlyabout2inches(or5centimeters),soifyouare

quick,youstandagoodchanceatcatchingthem.Thistakespractice.Makesurenoonegetshit,eitherbythecoins

oryourarm.

3.Placeacoinonacardplaceddirectlyoverthebottle.Flickthecardawayandthecoindropsintothebottle.

4. Support a coin or sugar cube on the edge of an embroidery hoop balanced on the opening of a jar (or bottle).

Smoothlypullingthehoopwillresultinthecoinorcubefallingintothejarbelow.

5.Slideanairpuckoraslideronanair track. (Anairhockey tablecanalsowork.)Without friction,anobjectkeeps

moving inastraight lineuntila force interactswith it, justasanobject inspace.Thisdemonstrates theaspectof

Newton’sfirstlawthatreferstoabodyinmotionstayinginmotion.

ThePoint

ThisprojectexploresNewton’sfirstlaw,whichisalsoknownasthelawofinertia:abodyatresttendstostayatrestunless

acteduponbyanexternalforce.Abodyinmotiontendstostayinmotioninastraightlineunlessacteduponbyanexternal

force.

105

Project25

Newton’ssecondlaw.Forcinganobjecttoaccelerate.

TheIdea

This classic experiment explores the connection between an object’s acceleration and the force applied to it. This

fundamentalprincipleofphysicswasfirstformulatedbySirIsaacNewtoninthefamoussecondlawofmotionthatbearshis

name.Tomeasureacceleration, youuseeither thestopwatchor themotionsensor techniqueofmeasuringacceleration,

whichweusedinpreviousexperiments.TheforcewillbeprovidedcourtesyoftheEarth,intheformofthegravitationforce

onamasshangingfromastring.

WhatYouNeed

low-frictioncart(oranairtrackandglider,ifavailable)

springscale

massset(including50g,100g,200g)

tape

string

pulley(lowmassandlowfrictionispreferable)

clamptoattachthepulleytothetable

tabletop(atleast1meterinlength)

stopwatchandmeterstickormotionsensor

Method

1. Determinethemassofthecartingrams.Divideby1000togetkilograms.

2. Placea100g(0.1kg)massinthecart.Secureitwithtape,ifnecessary.

3. Setthecartatoneendofthetable,andattachthepulleytotheotherend.

4. Attachthestringtothecart,runitoverthepulley,andtiealoopthatextendsafewinchesbelowtheedgeofthe

table,intheotherend,asshowninFigure25-1.

5. Whileholdingthecartinpositionatthefarendofthetable,hangamassontheloopontheothersideofthestring.

6. Next,youreleasethecartandlettheweightofthehangingmasspullthecartacrossthetable.Asyoudothis,you

measuretheaccelerationofthecartusingeitherofthepreviousmethods:

–Stopwatch:measurethetime(inseconds)forthecarttobepulledameasureddistance(inmeters).Theacceleration

(inm/s2)isdeterminedbya=2d/t2,wheredisthedistancethattheobjectispulledacrossthetable(inm)duringtime,

t(inseconds).

106

Figure25-1Newton’ssecondlawapparatus.CourtesyPASCO.

–Motionsensor:recordthepositionofthecartasit isdrawnacrossthetable.Displaythevelocityversustimegraph

anddeterminetheaccelerationofthecartbyfindingtheslopeofthatgraph.ThiscanbedoneeitherusingtheSlope

toolfromtheDataStudiomenuormoresimplybyobtainingtheaccelerationasthechangeinvelocitydividedbythe

changeintime.

7.Repeatthismeasurement,butmakethefollowingchanges:

–Varythemassinthecart,butkeeptheappliedforceconstant,asindicatedinFigures25-2and25-3.

–Varytheappliedforcebyaddingorremovingsomeofthehangingweight,butkeepthemassinthecartconstant,as

showninFigure25-4.

Figure25-2Findingaccelerationasafunctionofmass,whilekeepingtheforceconstant.CourtesyPASCO.

Figure25-3Addingmasstothecartwhilekeepingtheforceconstant.CourtesyPASCO.

Figure25-4Accelerationasafunctionofthehangingmass.CourtesyPASCO.

ProvingNewton’ssecondlaw

Newton’ssecondlaw,whichstatesthatF=ma,orasNewtonoriginallyputit,a=F/m.

mrepresentstheentiremassofthesystemandincludesthemassofthecart(mc),plusthemassinthecart(m1)

plusthehangingmass(m2).

Fistheappliedforcethatpullsthecartandisgivenbythehangingmass,m2(inkilograms,notingrams)timesthe

gravitationalacceleration(9.8m/s2).(Togetkilogramsfromgrams,dividethenumberofgramsby1000.)

aistheacceleration(inm/s2)oftheentiresystem,includingthecart,itscontents,andthehangingmass.

Youcanusethefollowingtoorganizeyourdata:

107

ExpectedResults

Theeffectofforceonacceleration

For a fixedmass in the cart (m1), the greater the applied force, the greater the acceleration. The expected relationship

betweenaccelerationand force isshown inFigure25-4,which (forsimplicity)shows theeffectof increasing thehanging

massonacceleration.(Theactualdrivingforceisgiveninnewtons,whichissimply9.8timesthemassinkilograms.)Without

friction(andtotheextentthatfrictioniseliminatedfromthisexperiment),thisshouldbealinearrelationshipasindicatedin

Figure25-5.

Figure25-5Predictedaccelerationversusappliedforcefordifferentvaluesof(total)mass.

Theeffectofmassonacceleration

Foragivenappliedforce,theheaviertheload,thesmallertherateofacceleration.Thisisaninverserelationship,asshown

inFigure25-6.

Experimental results for acceleration for a given mass and applied force come close to the predicted results if the

frictionalforcesarenotsignificant.Evenwithfriction,itcanstillbeshownthataccelerationdependsonappliedforceandis

inverselyproportionaltothemass.Frictionincreaseswhentoomuchmassisplacedinthecart.However,ifthemassistoo

small,theaccelerationcanbesohigh,itbecomesmoredifficulttomeasureaccurately.

Useoflow-frictiontracksreducestheamountoffriction.Motionsensorsprovideanicewaytodeterminetheacceleration.

Figure25-7showstheresultofmotionsensordatafortwodifferenttotalacceleratedmasses.

108

Figure25-6Predictedaccelerationversustotalmass.

Figure25-7Velocityversustimefortwodifferentmassesacceleratedbyaconstantforce.Theslopeofthev-tcurvegives

theacceleration.CourtesyPASCO.

WhyItWorks

Newton’ssecondlawstatesthatF=maora=F/m.Moreforceleadstogreateracceleration,butmoremasslowerstherate

ofacceleration.

OtherThingstoTry

YoumaywanttoconsiderdoingthisusingaHoverPuckdrawnacrossthefloorbyamasshungfromapulley,asshownin

Figure25-8.Asbefore,remembertoincludethemassoftheHoverPuckaspartofthetotalsystemmassbeingaccelerated.

Thehigherthepulley issupportedabovethefloor,thelongertherunyoucanhaveacrossthefloor.Aqualitativebutvery

intuitivewayofshowingtherelationshipbetweenaforceandaccelerationcanbeshownusinganLEDaccelerometer.The

constantforcefromthefanresults inanaccelerationindicatedbytheLEDsasshowninFigure25.9.Thedirectionofthe

forcevectorisinthesamedirectionastheaccelerationvector.

109

Figure25-8UsingaHoverPucktoproveNewton’ssecondlaw.

Figure 25.9 The fan exerts a force which accelerates the cart. The LEDs on the accelerometer show how the cart

accelerates.CourtesyPASCO.

ThePoint

The result here is one of the most significant results in physics: a force causes acceleration. For a given mass, the

accelerationofanobjectisproportionaltotheappliedforce.Foragivenforce,theaccelerationisinverselyproportionalto

theamountofmass.

110

Project26

Newton’sthirdlaw.Equalandoppositereactions.

TheIdea

IfSirIsaacNewtonhadaskateboard,itmighthavesavedhimsometimeindiscoveringhisthirdlaw,althoughNewtonmight

havehadsomuchfundoingit,hewouldn’thavehadtimetoinventcalculus.Thelawsofphysicsapplytoallobjects.Sports,

inparticular,canbethoughtofasintuitiveapplicationsoftheprinciplesofphysics.Thisexperimenttakesadvantageofthe

factthatallobjectsintheuniversefollowthelawsofphysics.WefocusparticularlyonNewton’sthirdlawandconservation

oflinearmomentum.

WhatYouNeed

2rollingchairs

or2peoplecapableofkeepingtheirbalanceonskateboards(eachwithhelmets);rollerbladeswillalsowork

medicineballoraseveralpoundmass,suchasabowlingball

safeplacetodothis

Method

1. Twopeoplefaceeachothersittinginthechairsonrollers,afewfeetapart.

2. Onepersontossesthemedicineballtotheother(bothareseatedinchairs).Feetshouldbekeptoffthefloor,so

thechairsarefreetomove.

3. Thetwopeopleagainfaceeachother.Onetriestopushtheother.Whathappens?

ExpectedResults

Thepersonwhocatchestheball,aswellasthepersonwhothrowstheball,willmovebackward.Similarly,thepersondoing

thepushing,aswellasthepersongettingpushed,willrecoilbackwards.

WhyItWorks

Momentumismasstimesvelocity.

Atthestartofthis,thetwoskateboardershavezeromomentum(theyhavemass,butnovelocity,sotheirmomentumis

zero).

Thevelocityoftheballtransfersmomentumfromthefirsttothesecondperson.Thefirstpersonrecoilsbackward.The

secondpersonalsomovesbackwardintheoppositedirection.

Another principle illustrated here is Newton’s third law: For every action (movement of the ball), there is an equal and

oppositereaction(recoilofthepersoninthechair).

OtherThingstoTry

Thepreviousdemonstrationscanbedonebyskateboardersorrollerbladers.(Pleaseremember,althoughweareinterested

inhorizontalactionandreactionhere,gravityisstillactiveintheverticaldirection,sokeepyourbalance.)

111

Mousetrapandtennisball

Conservationof linearmomentumandNewton’sthird lawcanbedemonstratedbyattachingamousetraptoa low-friction

cart.Thetrapissetandatennisballispositionedinplaceofthecheese.Whenthemousetrapisreleased,theprocessof

tossingtheballresultsintheequalandoppositereactionofthemousetraprecoilinginabackwardmotion.Thisisshownin

Figure26-1.Boththemousetrapandtheball initiallyhavezeromomentum.Themomentumoftheballgoingtothe left is

equalbutoppositetothemomentumofthemousetrapandcartmovingtotheright.

Figure26-1Equalandoppositereactions.

Fancar

Puttingapropelleronacartwithwheels,asshowninFigure26-2,propelsthecartforward(orbackwardifturningtheother

way).

Whatwouldyouexpecttohappenifasailisputinfrontofthepropellertocatchtheair,asshowninFigure26-3?Some

peoplewouldsaythecartwillmovefasterbecausetheforcefromthefanwill“push”thecart.However,whatwefindisthis:

withthesailinplace,thecartdoesnotmoveasitdidwithoutthesail.Thisisasurprisingresultformanypeopleseeingthis

forthefirsttime.Thereasonforthisis,withoutthesail,theequalandoppositereactionofthepropellercausesthecartto

moveforward.However,withthesailinplace,theforceofthepropellerbalancesthereactionforce.Asaresult,thereisno

netforceandthecartdoesnotmove.

Figure26-2Withouta“sail”thefanpushesthecart.

112

Figure26-3Witha“sail”thecartdoesnotmove.

ThePoint

Linearmomentumisconservedintheabsenceofexternalforces.Foreveryaction,thereisanequalandoppositereaction.

113

Project27

Newton’sthirdlaw.Bottlerockets.Whydotheyneedwater?(SirIsaacNewtoninthe

passenger’sseat.)

TheIdea

Inthisexperiment,youlauncha2-litersodabottleintotheair.Yourfueliswater,whichispropelleddownwardbyairpressure

forcing the rocket upward. This experiment is a good illustration of Newton’s third law and the law of conservation of

momentum,anditlendsitselftoanice,friendly,competitive“spacerace.”

WhatYouNeed

2-litersodabottle(waterbottlesarenotnecessarilycapableofsustaininginternalpressure,assodabottlesare)

noseconefabricatedfromacardboardpartyhatoraconeformedfromposterboardandtape

cardboardforfins

gluegunortape

water

hardrubberstopperthatjustfitsthetopofthebottle(thestoppershouldbesnugenoughtosealthebottlewhileit

isbeingpressurized,butnotoversizedtotheextentthatitpreventsthebottlefromlaunching)

bicyclepumpwithaone-wayvalve(oranelectricpumporcompressor)

optional: support toserveasa “launchpad” for thebottle (for instance,made froma tripodbuilt fromPVCpipe

sections).SeeFigure27-1.

Method

Buildtherocket

1.Slidetheopenendofthebottleovertheverticalrodofaringstandforeasierassembly.

2.Usetheglueguntoattachfinstotherocket(rememberingthattheflatsideofthebottleisthetopoftherocket).Be

carefulnottoapplyexcessiveheat,whichcouldmeltaholeinthebottle.

3.Attachanoseconetomakethebottlemoreaerodynamic.Useposterboardoraconeshapedpartyhat.

114

Figure27-1Bottlerocketreadyforlaunch.

4.Fillthebottlefromaboutone-quartertoone-thirdfull.

Assemblethelauncher

Youcandothisinseveralways.Ifyouareplanningmanylaunches,youmaywanttogoforsomethingmoreelaborate.The

basicpartsare:

1.Anairpumporcompressor.

2.Aone-wayvalve:Thesimplestwaytodothisistoinsertaneedle(availableatanysporting-goodssupplystore)used

toinflatefootballsandbasketballsthroughthestopper.Withthismethod,noreleasemechanismisneededbecause

therocketwilltakeoffassoonasenoughpressurebuildsuptoovercometheforceholdingthestopperinthebottle.

3.Areleasemechanism:Ametal“claw,”whichholdsthebottleinplaceuntilthepressurebuildstoacertainlevel,allows

agreaterpressuretobuildupinthebottle.ThiscanbemountedonawoodenorPVCtripodstructure.Youcanalso

holdthisinyourhand,butbepreparedtogetwetasthe“fuel”surgesdownwardfromthebottomoftherocket.

Launchtherocket

1. Insertthestopperintothebottle.

2. Securethebottleontothelauncher.Movetheholdingmechanismintoplace(orholditifthatiswhatyouaredoing).

3. Pressurize thebottle.Themaximumairpressureshouldnotgoabove80 to100psi (poundspersquare inch) to

avoidburstingthebottles.

4. Useastringtoremotelyreleasethereleasemechanism.

ExpectedResults

Therocketwillascendvertically.Theupwardlegpathcantakeaslongasabout4secondscorrespondingtoamaximum

heightofmorethan75meters(over250feet).

WhyItWorks

115

Theair pressure forces thewaterdownwardwithahigh velocity.Themassof thewater times the velocityof thewater

representsthedownwardmomentumofthewater.Conservationofmomentumrequiresanequalmomentumupwardthatis

appliedtothemassofthebottle,whichacquiresavelocitytotakeitupward.Anotherwaytosaythisistheactionofthe

downwardforceofthewateriscounterbalancedbyanequalandoppositereactionthatdrivesthebottleupward.

OtherThingstoTry

Bottlerocketscanbemademoreelaboratebyaddingfins.Aparachute,madeoftheclearplasticusedbydrycleaners,can

beaddedtokeeptherocketintheairforalongertimeortoreleaseapayloadconsistingofatennisballorotherobject.

YoumaywanttoseetheMythbustersepisode,wheretheyexploretheuseofbottlerocketstopropelaperson.Note,for

safetyreasons,theyconfinedtheireffortstodummies.

ThePoint

ThisisanotherexampleofconservationoflinearmomentumandNewton’sthirdlaw.

Figure27-2SirIsaacNewton’slawsofmotiondescribethemotionofbottlerockets,satellitesandplanets.

116

Project28

Pushingwater.Birdsflyinginsideatruck.

TheIdea

Newton’sthirdlawstatesthatforeveryaction(force),thereisanequalbutoppositereaction(force).Thisprojectillustrates

howthisconceptcanbeapplied toaparticularphysicalsituation.Theoutcomemaybedifferent thanwhatmanypeople

expect.

WhatYouNeed

1ping-pongballattachedtoastring

2beakers(orjars)filledwithenoughwatertoimmersetheping-pongball

balancescale

counterweights

Method

1.Seteachofthebeakersontheopposingpansofthescaleandestablishabalance,asshowninFigure28-1.

2.Predictwhatwillhappenwhentheping-pongballisloweredintothebeakerofwater.Willthesidewiththepingpong

ball

a.Rise?

b.Fall?

c.Remainbalanced?

3.Lowertheping-pongballintothebeakerandobservewhathappens.

4.Removetheping-pongball.Whatistheeffectonthebalance?

ExpectedResults

Loweringtheping-pongballintothebeakerforcesthatsideofthebalancedown,asshowninFigure28-2.

Whentheping-pongballiswithdrawn,thebalanceisrestored.

WhyItWorks

Thereisabuoyantforceonanyobjectimmersedinwater(orpartiallyimmersedinwatersuchasafloatingping-pongball).

Foreveryactionthereisanequalandoppositereaction.Inthiscaseiftheaction(thebuoyantforce)isup,thereactionmust

bedown,causingtheobservedeffect.

117

Figure28-1Whatwillbetheeffectofafloatingobject?Willittipthebalance?

Figure28-2Newton’sthirdlaw:Thebouyantforcepushesup.Theoppositereactionpushesthescaledown.

OtherThingstoTry

Thisissimilartotheenigma:ifbirdsareinatruck,willthetruckweighlessifthebirdsareflying,insteadofatrestonthe

floorofthetruckbed?Itturnsoutthattheforceexertedbythebirds’wingsexertsthesamedownwardpressureonthetruck

bedastheweightofthebirdsatrest.(Aswiththepreviousexperiment,thisisalsoaddressedbyaMythbustersepisode.)

ThePoint

ThisexperimentshowshowareactionforceisestablishedbyNewton’sthirdlaw.

118

Project29

Slippingandsliding.

TheIdea

This project compares the amount of friction developed by various common substances. It also shows a simple way to

measuretheamountoffriction.

WhatYouNeed

book

coin

icecube

rubbereraser

protractor

Method

1. Lineallthreeobjectsupinastraightlineonthebook.

2. Slowlyliftthebook.

3. Asyouraisethebook,notetheanglewhereeachoftheobjectsjustbeginstoslide.

4. Breaktherubbereraserintovariouspiecesofdifferentareas.

5. Lineuptheeraserpiecesanddeterminethesequenceinwhichtheyslide.

6. Breaktheicecubeintovarioussizedpiecesindifferentareas.

7. Linetheeraserpiecesupanddeterminethesequenceinwhichtheyslide.

ExpectedResults

Theicegoesfirst,thenthecoin,andthen,finally,theeraser.

Foragivenmaterial,thecontactareabetweentheslidingsurfacesdoesnotsignificantlyaffecttheforceoffriction.

WhyItWorks

The surface of each material is characterized by a different amount of friction. It would be nice if this was called the

surface’s“slipperiness.”However,itgoesunderthemoreprestigiousnameofcoefficientoffriction,whichistheamountof

frictionalforceasurfaceimposesonanobjectcomparedtoitsweight(onahorizontalsurface).Thereisafrictionalforceto

getsomethinggoing(staticfriction)andaforcetokeepsomethinggoing(kineticfriction).Thefrictionalforcedependson

thecoefficientoffrictionandthe(horizontal)weightoftheobject.Itdoesnot(tofirstorder)dependonthecontactarea.

Theconditionfortheobjecttoslideisthatthetangentoftheangleequalthecoefficientof(static)friction.Byfindingthe

anglewheretheobjectjustbeginstoslide,youcanfindthecoefficientofstaticfrictionbysimplytakingtheinversetangent.

(Thisisthekeyonyourcalculatorthatsaystan−1,arctanoratan.)SeeFigure29-1.

119

Figure29-1Forcesonanincline.

OtherThingstoTry

Frictionappliesa force thatputs thebrakesonmotion.Theamountof frictionbetween twosurfaces ischaracterizedby

something called the coefficient of friction, which is represented by the Greek letter μ (mu pronounced “myoo”). On ahorizontalsurface,theforceexertedbyfrictionisequaltotheweightoftheobject,multipliedbythecoefficientoffriction.

Thereare two types—static friction,whichmust beovercome toget somethinggoing,andkinetic friction,whichmust be

overcometokeepsomethinggoing.

Inthisproject,theobjectsslidedowntherampifthetangentoftheangleisgreaterthanthecoefficientofstaticfriction

forthatobjectonthebook.Thisconditioncanbeturnedaroundand,iftheslidingangleisfound,thecoefficientoffriction

canbeeasilyandsimplydetermined.

Afollow-upalongasimilarthemeistopredictwhetheranobjectcanslidealongasurfacewithouttoppling.Abooksliding

frontsidedownonasmoothtablewillnothavestabilityproblems.Butacanoftomatojuiceslidinguprightacrossarough

woodenfloormaybeanotherstory.Trythiswithseveralcylinderswiththesamediameter,butwithdifferentheights.Sections

of cardboard tubes or plastic pipe sections are good to test this. The condition for sliding without tipping is that the

coefficientof(kinetic)frictionbelessthantheratioofthediameterofthecylindertoitslength.

Youcouldalsodesignanexperimenttostudytheeffectofincreasingtheweight,surfacearea,andvelocityofmotion.You

willfindtheweightoftheobjectistheonlysignificantvariableand(surprisingly,formanypeople)thecontactareais(almost

entirely)insignificant.

ThePoint

Frictionisaforcethatopposesmotion.Onahorizontalsurface,theamountoffrictiondependsontheweightofanobject

pressingitincontactwiththatsurface,andthecoefficientoffriction.

120

Project30

Springs.Pullingback.Thefurtheryougo,theharderitgets.

TheIdea

Theforceexertedbyaspring,unlikeanyoftheforceswehaveencounteredsofar, isnotconstant.Itcontinuouslyvaries.

Thefurtheryoupullthespring,theharderitpullsback.ThisrelationshipisknownasHooke’slaw.Becauseofthis,springs

havethecapabilitytokeepgoingbackandforthuntilfriction(eventually)slowsthemdown.

WhatYouNeed

varioussprings

massset(oraspringscale)

metricruler

Method

Measurethespringconstantofaspringbyfollowingthesesteps:

1. Suspendthespringfromthesupport.

2. Locatethedistancefromthebottomofthespringjusthangingunderitsownweight.Thisiscalledtheequilibrium

point.

3. Hangamassfromthespring.Themassshouldbechosensoitincreasesthelengthofthespringbynogreaterthan

about50percent.

4. Measurethedistance(incentimeters)thebottomofthespringispulledbelowtheequilibriumpoint.SeeFigure30-1.

5. Find the force. If your reading is in grams, convert it to newtons by dividing themass in grams by 1000 to get

kilograms,andmultiplyingby9.8togetforceinnewtons.Itmaybeeasiertodothisusingaspringbalancetoget

theforce topull thespringacertaindistance.Manyspringbalancesarecalibrateddirectly innewtons,so in that

case,thereisnoneedtoconverttheforceintonewtons.

6. Thespringconstantcanbedeterminedbydividingtheforcebythedistanceaccordingtotheequation:k=−F/x.(Note:thenegativesignaccountsforthefactthattheforceandtheextensionareinoppositedirections.Ifyoupull

up, thedistance ispositive,but the force isnegative.Regardlessofhowyoudo it, thespringconstant isalways

positive.)

121

Figure30-1Determininghowstiffaspringisbymeasuringthespringconstant.

ExpectedResults

Thestifferthespring,thehigherthespringconstant.Asanexample,ifittakes10newtonsofforcetostretchaspringby1

centimeter,thespringconstantwouldbek=10N/1cm=10N/cm.Itwouldtake20newtonstostretchthatsamespringby2

centimeters. The spring constant should prove to be constant and establish a linear relationship between force (F) and

extension(x).RealspringshavealinearrangeoverwhichHooke’slawisareasonableapproximation.Ifyoustretchtoofar,

however,youwillgooutofthelinearrangeanditusuallytakesaninitialforcetobringthespringintoitslinearrange.

WhyItWorks

Overmostofitsrange,theforceexertedbyaspringisdirectlyproportionaltotheamountitisdisplacedfromitsequilibrium

position.Thespringconstant isaway tocharacterizehowmuchaparticularspringexerts foragivendisplacement from

equilibrium.

OtherThingstoTry

A more accurate value for the spring constant can be determined by taking several readings and plotting force versus

displacement,andthenfindingtheslopeoftheline.

ThePoint

The forceexertedbyaspring isproportional to thedistance thespring isstretched.The furtheryoupull, thegreater the

forcethespringexertsintheoppositedirection.

122

Project31

Atwood’smachine.Averticaltugofwar.

TheIdea

The Atwood machine illustrates some aspects of force and acceleration. Like an incline, the Atwood machine slows

accelerationdowntoameasurableandobservableamount.ThisprojectshowshowtheAtwoodapparatuscanbeusedto

studyacceleration.

WhatYouNeed

pulley

supportforpulley,suchasaringstand

string

variousmasses

Method

1. Setuptheapparatuswitheachoftwomassesattachedtostringandsuspendedoverapulley,asshowninFigure

31-1.

2. Releasethemassesandobserve/measuretheirmotion.

3. Asinpreviousexperiments,theaccelerationofthemassescanbemeasuredusingthestopwatchmethod(usinga

=2d/t2) or determining the acceleration using a motion sensor. (Different combinations of masses can also be

comparedandrankedvisuallywithoutdetailedmeasurements.)

ExpectedResults

Thegreaterthedifferencebetweenthetwomasses,thegreatertheacceleration.

Thegreaterthecombinedmasses,thesmallertheacceleration.

Theaccelerationforthetwomassesis:

123

Figure31-1Atwood’smachine.

Ifm1isthelargermass,theaccelerationisinthedirectionofthelargermassgoingdown.

WhyItWorks

The force on the system is F = g(m1− m2). According to Newton’s second law, this equals the total mass times theacceleration.Becausethetotalmassis(m1+m2),wecanderivethepreviousexpressionforacceleration.

OtherThingstoTry

Onceyougettheideaofthis,tryitatanincline,asshowninFigure31-2.

Predictwhatangleorcombinationofmasseswillresultinequilibrium.

Because frictionhelpsestablishstability,awindow isaround thepredictedconditions thatwillalso result inequilibrium.

Thiscanalsobedonewitheachofthetwomassesslidingonanincline.

ThePoint

AnAtwoodmachinedemonstrates theprinciplesofNewton’ssecond law.Thenet forceon themassescauses the total

massofthesystemtoaccelerate.

124

Figure31-2Atwood’smachineonanincline.

125

Project32

Terminalvelocity.Fallingslowly.

TheIdea

Shortlyafterjumpingfromanairplane,skydiversreachasteadyvelocityinsteadofconstantlyacceleratingasdoothermore

streamlinedobjectssubjected toEarth’sgravity.When thishappens, theskydiver fallsata terminal velocity that isnearly

constant.Thisisfortunatebecause,oncetheparachuteopens,itismucheasiertoslowtheskydiver’sfall.Hadtheskydiver

beenarockinavacuumwithoutthebenefitofairresistance,itwouldreachamuchhighervelocity.

WhatYouNeed

coffeefilter

meterstick

stopwatch

coin,book,oranothercompactobject

optional:motionsensor

Method

1. Dropacoffeefilterfromameasureddistance.

2. Comparethetimeittakestofallwithacoinorabook.

3. Comparethedistanceversusthetimegraphgeneratedbyamotionsensorforeachofthetwoobjects.

ExpectedResults

Notonlywillthecoffeefiltertakelongertodescend,butmoresignificantly,itfallsatasteadyvelocity.Thecoin,typicalof

other objects in free-fall, accelerates as it falls and will have an ever-increasing velocity. The following shows distance

versustimeandvelocityversustimegraphsforthesetwoobjects.Noticethefallingbookcontinuestoaccelerateasitfalls.

Thisisindicatedbythecurvedshapeoftheposition-timegraphandthepositiveslopeforthevelocity-timegraph.

126

Figure32-1Fallingbook.

127

Figure32-2Fallingcoffeefilter.

The coffee filter falls with constant velocity. The position-time graph is a straight line and the velocity-time graph is

essentiallyahorizontalline,indicatingaconstantvelocityduringthedescent.

WhyItWorks

When a falling object encounters significant air resistance, the faster the object falls, the greater the force opposing its

descent.So,themoregravitytriestopulltheobjectdown,themoredeterminedtheairresistanceistoopposegravity.Asa

result,equilibriumisestablishedwiththeobjectfallingataconstantterminalvelocity.

OtherThingstoTry

Comparethedescentofbottlerockets(describedinProject27)withandwithoutparachutes.

ThePoint

Free-fallisdifferentthananobjectsubjectedtodragforces.

Anobjectinfree-fallaccelerateswithaconstantrateof9.8m/s2.Anobjectsubjecttoadragforcedoesnotaccelerate,

butreachesasteadyconstantvelocity,calledtheterminalvelocity.

128

Project33

Balancingact.Painteronascaffold.

TheIdea

Ascaffoldisbuiltfromaboardplacedacrossabasewithoutanythingholdingitdown.Howfarfromtheedgeoftheboard

canapainterstandwithouttippingtheboard?Thisexperimentinvestigatestheconditionforstabilitycalledstaticequilibrium.

WhatYouNeed

sectionofa2″×4″blockabout6″longmeterstick

20gmass

Method

1. Settheblockonthetable.Thiscanbeeitherwiththe2”edgeparalleltothetableorthe2”edgeperpendicularto

thetable.Eachcasegivesadifferentresult.

2. Measurethemassofthemeterstick.

3. Laythemeterstickovertheblock,asshowninFigure33-1,withthe50-centimetermarkofthemeterstickcentered

overthemiddleoftheblock.

4. Predicthowfarthe20-grammass(the“painter”)canbeplacedfromthecenterwithouttippingthemeterstick,asis

thecaseshowninFigure33-2.

5. Theprincipletouseisthatthetorquetryingtotipthe“scaffold”mustnotbegreaterthanthetorquethatholdsitin

place.Herearetheformulas:

Tippingtorque

1w1

2w2

d1=distancefromedgeofblocktocenterof20gmass

w1=weightofblock

d2=distancefromedgeofblocktothe50cmmarkofthemeterstick

w2=weightofthemeterstick

A2″×4″blockhasactualmeasurementsof1½″×3½″(or3.8cm×8.9cm).(The3.8cmsideistheheightandthe8.9cmsideisthewidthoftheblock.)Thedistance,d2,isone-halfthesupportingedge.Thiswouldbe4.45cm(withthe

widthoftheblockalongthetable)or1.6cm(withtheheightoftheblockonthetable).

6.Tryitwithothermasses.

129

Figure33-1Howfarcanthe“painter”movetowardtheedgeoftheboard?

Figure33-2Herethe“painter”hasgonetoofar.

ExpectedResults

For a 90-grammassmeterstick balanced on top of a nominally 2”× 4” block, the following table shows themaximumdistancethepainter,m2,cangowithouttopplingthemeterstick.

WhyItWorks

Theamountofmasscarriedatapointofsupportistheresultofatorquegeneratedaroundthepivotpoint.Inthiscase,the

springscalesformapivotpoint.Thegreaterthemasssupported,andthefurtherfromthepivotpoint,thegreaterthetorque.

OtherThingstoTry

130

Howweightisdistributed

Placetwobathroomscalesonthefloorseparatedbythelengthoftheboard.Setastiffboardabout8feetlongovereach

scale.Adjust thescalestoreadzero, toeliminatetheeffectof theweightof theboard.Predictandmeasurethereading

directlyoverthescales,inthemiddle,andatarbitrarypositionsinbetween.

Figure33-3

Verticalstaticequilibrium

AssembletheapparatusshowninFigure33-3.Basedonbalancingclockwiseandcounter-clockwisetorque,developother

combinations that establish equilibrium. This is based on a demonstration found on the U.C. Berkley Physics Lecture

Demonstrationwebsitehttp://www.mip.berkeley.edu/physics/noteindex.html(item:A+60+0).

ThePoint

Staticequilibrium reflectsabalanceof forces that results inacollectionofobjects remainingstableandstationary.The

conditionforstaticequilibriumisthatthesumoftheforceandthesumofthetorquesonanobjectiszero.

131

Project34

Hangingsign.

TheIdea

Youarehangingasignforyourcaféthatweighs50pounds.Youhaveonecablethatis4feetlongandanothercablethatis5feetlong.Whichonesupportsmoreoftheweight?

Anglescomplicatehowforcesaredistributed.Thisprojectexploresasimplesituationsimilartohangingasignwithtwo

differentlengthcables.

WhatYouNeed

2springscales

mass—(shouldgiveclosetoafull-scalereadingintheverticalpositiononyourspringscales)

string

2ringstandswithclampsorcomparablesupport

keyring

protractor

Method

Symmetricalsign

1. Placetheringstandsabout18inchesapart.

2. Cuttwoequal-lengthsectionsofstring.Thestringsshouldbe8inches,leavingacoupleofinchesoneachsidefor

attachingtothesupportandtheweight.

3. Setthespringscalestoreadzero(inthepositiontheyarebeingused),withnoweighthangingfromthem.

4. Hookbothofthespringscalestoeachoftheringstands.

5. Attacheachstring—onesidetothekeyringandtheothersidetotheclampontheringstrand.

6. TheapparatusshouldbeasshowninFigure34-1.

7. Hangthemassonthekeyring.

8. Recordthereadingoneachofthespringscales.

9. Repeat,usingdifferentmassesanddifferentstringlengths.

Asymmetricsign

1. Repeattheprevioussteps,usingdifferentstringlengths.

2. Basedonyourevaluation,canyouanswerthequestionposedatthebeginningofthissection?

132

Figure34-1

ExpectedResults

Inthecaseofthesymmetricsupports,thetwoscaleswillreadthesame.

Ifthestringsaredifferentlengths,theshorterofthetwostringswillbearmoreoftheweight.

WhyItWorks

Theforceinacableisthecombinationofthevariousforcespresent.Theoverallforcedependsonhowlargeeachofthe

forcesisanditsdirection.Themethodofcombiningtheseforcesiscalledvectoraddition.

OtherThingstoTry

Tensionistheforceinaropeorcablethatcanchangedirectionwithoutlossesbygoingaroundapulley.Howdoyouthink

theforceineachofthecasesinFigure34-2compares?Testitoutwithweightsandpulleys.

Eachspringscaleshouldread9.8newtons,whichistheamountofforceexertedbygravityona1kgmass.

Tugofwar.Itisalmostimpossibletopullaropesupportingamoderateweighttightenoughtobeperfectlyhorizontal.The

experimentalsetupisshowninFigure34-3.Agallonmilkcontainerfilledwithwatermakesagood4kgmasstotrythiswith.

133

Figure34-2Howmuchforceismeasuredbyeachofthespringscales:A,B,andC?

Figure34-3Witha4kgmass,itisalmostimpossibletopulltheropeperfectlyhorizontal.

Tobringtheropetowithin5degreesofhorizontalwitha4kgweightinthemiddle,youneedtopullwithaforceof560

newtons(orover125pounds).Tobringtheropetowithin1degreeofhorizontal,youneedtoapplyaforceofabout2300

newtons(orover500pounds).

ThePoint

Thisexerciseshowshowaforcecanbebrokendownintoorresolvedintoapairofcomponentforces.Thedownwardforce

from the suspended sign is supported by cables of various lengths in various directions.This is the typeof thinking civil

engineersapplyonadailybasis—tooversimplify,howstrongsomething(likeabridgecable)needstobetosupportaload

(liketheroadsurfacewithcars).

134

Project35

Pressure.Implodingcans.

TheIdea

Howpowerfulisairpressure?Wecananswerthisbyobservingwhathappenswhenweremoveairfromwhereitisnormally

found.

WhatYouNeed

emptysodacans

oralargerrectangularcanwithascrew-oncap,ifyoucangetone.(Theseareusedforcookingoilorpaintthinner,

andtheycanbepurchasedtodothisexperiment.)

hotplate

beaker

water

ovenmittorbeakertongs

pailofcoldwater

Method

1.Rinsethecan,soitisreasonablyclean.

2.Putasmallquantityofwater(2tablespoons)inthecan.

3.Placethecanonthehotplateandkeepitthereuntilthewaterboilsandsteamcomesoutofthecan(Figure35-1).

4.Carefullyremovethecanfromthehotplateusingthemittortongs.

5.Quicklyimmersethesodacan,withsteamstillevolving,topsidedowninthewater.Observewhathappens(Figure35-

2).

Figure35-1Asmallamountofwaterinthecanisheated.

135

Figure35-2Lowerairpressureinthecancausesittobecrushed.

6.Removetherectangularcanfromthehotplate.Withsteamstillcomingoutofthecan,screwonthecap.Waituntilit

cools intheairorfacilitatethecoolingwithwateror ice. (Ifyouaredoingthisasademonstration,thismaytakea

while and a sense of drama can be created by pretending that nothing is happening and going on to the next

experiment.)

ExpectedResults

Thesodacanwillbecrushedalmostinstantaneously.Therectangularcanmaytakeafewminutes; itgetscrushedslowly

(asifbyaprotégéofDarthVaderusingtheForce).

WhyItWorks

Airexertsapressureof14.7poundsoneverysquareinch.Asthesteaminthecanscondenses,theairpressureinsidethe

candropsandthereisadifferenceinpressurebetweentheinsideandoutsideofthecan.Thisisprimarilytheresultofthe

changeinstatefromvaportoliquidandtoalesserdegreefromthecontractionofthegasinthecanasitcools.Thismeans

asodacan(6.5incheshighand3inchesindiameter)hasaforceofover900poundspressingdownonitssides!

OtherThingstoTry

Trythiswitha55-gallondrumasshowninFigure53-3.Useavacuumpumpconnectedtothedrumthroughavalvetocreate

thepressuredifference.Thismaytakesometime,butitwillbeworththewait.Youmaywanttowarnthepeopleyouwork

withthattheboomtheyareabouttoheardoesnotrequiretheemergencyresponseteamtobesentin.

ThePoint

Airpressureissubstantial,exertingaforceofnearly15poundsforeverysquareinchthatitisincontactwith.

136

Figure35-3Airpressuredidthis.

137

Project36

Pressure.Supportingwaterinacup.

TheIdea

Whichweighsmore:anemptycuporafullcup?Obviously,thefullcup.So,ifyouturnacupupsidedownwithaflatcover,

which has the better chance of being supported: the (lighter) empty cup or the (heavier) full cup?Many people find the

outcomesurprising.

WhatYouNeed

cuporbeakerwithaflat,circular,smoothtop.(Ifthebeakerhasaspout,itshouldbeflatenoughsoitcanmake

contactwithacardatallpointsalongitstopsurface.)

watertofillthecup

flat,stiff,lightweightsquare,largeenoughtocovertheentiretopsurfaceofthecup.Thesquareshouldnotbecome

waterlogged.Cardboardisnotthebestchoice.Foamboardstandsuptowaterbetter.Indexcardscanwork,butyou

mustbecarefulnottoletthemflexandbreakthesealwiththecup.

Method

1. Startwith theempty cup.Cover theempty cupwith the square.Turn it upside downandobservewhat happens

(Figure36-1).

2. Withthecupstillempty,moistenthetopsurfaceofthecuptomakeitmoresticky.Coverthecupandturnitupside

down.Whathappens?

3. Nowfill thecupwithwater to thebrim. Itwon’thurt tohave itgoabovethesurfaceof thecupor toallowsome

watertospillout.Coverthecupwiththesquare.Invertandobservewhathappens.

ExpectedResults

The squarewill fall off with the empty cup, evenwith the benefit of the surface being sticky. Thewater in the full cup,

however,willbeheldinplacebythesquare(Figure36-2).

WhyItWorks

Thewaterinabeaker5centimetersindiameterand12.7inchestallhasamassof250g(0.25kg)andweighs0.55pounds

(or2.5newtons).Theairpressureonthe5centimeter(roughly2inch)diametercircleisover3pounds.Theairpressureis

fargreaterthantheweightofthewaterinthebeaker.Theemptybeakerhasthesamepressureinsideandoutsidethecup,

sotheairpressureisbalancedandtheweightofthecupcausesittofall.Theadhesionofthesquaretothecupisclearly

notenoughtomakeupthedifference.

138

Figure36-1Withthecupempty,thereisnothingtoholdthesquareontothecup.

Figure36-2Theforceextertedbyairpressureisgreaterthantheweightofthewater.

OtherThingstoTry

Calculatehow tall theglasscanbewith thecardsupportedbyairpressure. (Thedensityofwater is1g foreverycubic

centimeterand1000gistheequivalentof2.2pounds.)Atmosphericpressurewillsupportacolumnofwater34feethigh.

Sincemercuryismoredensethanwater,atmosphericpressurewillsupportacolumnofmercuryabout30incheshigh.The

exactheightvarieswithlocalairpressureandprovidesawaytomeasurechangesinairpressure.

ThePoint

Airpressureislargecomparedtothepressureexertedbytheweightofacupofwater.

139

Project37

Pressure.Sometimesthenewscanbeprettyheavy.

TheIdea

Howmuch pressure does the atmosphere exert on a sheet of newspaper? As with the previous experiments, the force

exertedbyairpressurecanbesurprisinglypowerful.

WhatYouNeed

sectionofnewspaper

table

pieceofwoodabout12to24incheslongandroughly1to2incheswide.(Thewoodshouldbethinenoughsoitcan

bereadilysnappedinhalfbysomeonewhoisnotablackbelt.Itshouldalsobestiffenoughsoitwillbreakrather

thanflexifstuck.Arulerthatyouarewillingtodedicatetothecauseofscienceusuallyworks.)

Method

1. Placethepieceofwoodonthetable,extendingapproximatelyone-halfitslength.

2. Placeafewlayersofthenewspaperoverthewood.Layitoutsoitisasflataspossible.Removeany“airpockets”

thatyoucanunderthepaperandmakesuretheedgesareflat.

3. UsingyourbestMaxwellSmartkaratechop,strikethewood.Hitithardenoughtobreakthewood.Showitnomercy

(Figure37-1).

ExpectedResults

Manypeoplewouldexpect thewoodtopushthepaperupandthrowthepaperpartwayacrosstheroom.However, if the

paperisproperlysealedoverthewood,strikingthewoodresultsinthewoodbeingpinnedtothetableandbreakingapartas

ifitwereclampedtothetable.

WhyItWorks

Let’ssayyouhavea1-inchwiderulerthatextends10inchesunderthepaper.Thismeansthat147poundsofairpressure is

pressingdownon the ruler.About thesameasamedium-sizedpersonstandingon thepaperholdingdown the ruler.Air

pressureisthatstrong.Ifthisdoesn’twork,itisn’tbecauseofinsufficientairpressure.Therulermaynotbreakif:airleaks

underthepaperfromtheedges,thewoodistooflexibletobreak,orthewoodistoothicktobreak. It isunnecessary,of

course,toactuallybreaktherulertodemonstratethestrengthofairpressureonthepaper.

140

Figure37-1Breakingaboardwithonlyairpressureholdingtheothersidedown.

OtherThingstoTry

Air pressureonpapercanalsobeobservedpressingdownon thepagesofabook.After interleaving thepagesof two

similarbooks,itwillbeverydifficult,ifnotimpossible,topullthetwobooksapart.Thisisnottheresultofthefrictionofthe

pages,butitisadirecteffectoftheairpressureholdingthepagestogether.

Thepowerofairpressurecanalsobedemonstratedusingasuctioncupsuchasthoseusedtopopoutminordentsincar

sidepanels.Todothisyouwillneedanobjectwithasmoothsurface.Onegoodexampleisalaboratorystool.

1.Attachthesuctioncuptothetopsurfaceofthestool,asshowninFigure37-2.Makesurethesuctioncupsealstothe

topsurfaceofthestool.

2.Pulluponthesuctioncup.

Thesuctioncupshouldbeabletoliftanaverage-sizedstoolupofftheground.Thereisacommonmisconceptionthata

vacuum somehow pulls or “sucks” objects to it. This is not the case. Suction cups work because of a difference in air

pressurebetweentheoutsideofthesuctioncupandthelittleairtrappedunderthesuctioncup.Thepressureonasuction

cupthatis4inchesindiameter(assumingaperfectseal)wouldbegreaterthan150pounds.

ThePoint

Airpressureexertsaforceonasurfaceinproportiontoitsarea.

141

Figure37-2

142

Project38

Archimedes’sprinciple.Whatfloatsyourboat?

TheIdea

Doesironfloat?Clearlyacubeofiron,whichismuchdenserthanwater,willsink.Then,howisitpossibleforaboatmadeof

iron(orironalloy)tofloat?Inthisexperiment,youinvestigatetheforcesthatcounteracttheforceofgravitytoallowobjects

thataredenserthanwatertofloat.

WhatYouNeed

“boat”:ashallowplasticcup(suchasa¼poundcoleslawcontainer).Youcanalsouseapieceofwoodasyour

boat.

“lake”:aplastictrayorfishtankfilledwithwaterdeepenoughandwideenoughtofloatthe“boat”

“cargo”:smallweights,pennies(eachpennyhasamassof2.7g)

100mLgraduatedcylinder

Method

1. Measurethevolumeoftheboat.Youcandothisbygeometry,ifyouaresoinclined,oryoucandoitbyfillingthe

cupwithwaterandmeasuringtheamountofwatertodothis.

2. Thenumberofgramsofwaterthatoccupythevolumeoftheboatequalsthenumberofgramsofcargoitcancarry

justbeforeitsinks.

3. Testthisbyaddingtheamountofweightyoupredicted.Don’tforgettoincludetheweightoftheboatitself.Ifyou

usepennies,counteachas2.7grams(orweighthem).Asyouaddweight,becarefulnottotiptheboatoryouwill

capsizeitprematurely.

4. Compareyourpredictionwiththeamountofcargoyourboatcouldactuallycarry.SeeFigure38-1.

5. Weare takingaslight liberty here for thesakeof clarity by focusingon themass.What holds theboat up isa

buoyantforce,whichismeasuredinnewtons.Thebuoyantforceequalstheweightofthewater(alsomeasuredin

newtons)displacedbythefloatingobject.

ExpectedResults

Asaruleofthumb,forevery1mLthatanobjectisheldsubmergedbelowthesurfaceofthewater,thereisabuoyantforce

capableofsupporting1gramofmass.

Anequivalentwayofexpressingthisisanobjectwillfloatifthedensityoftheentireboat,consideringitsentirevolume,is

lessthanthedensityofthesamevolumeofwater.Thedensityofwateris1gram/cubiccentimeteror1000kilogram/cubic

meter.

Figure38-1Thebuoyantforceequalstheweightoftheboatplusitscargo.Thiscanbepredictedbydeterminingtheweight

143

ofthedisplacedwater.

WhyItWorks

Thebuoyantforceonanobjectisgivenbytheweightofthefluiditdisplaces.

Thebuoyantforceexertedonafloatingobjectequalsthevolumeofthatobjectthatissubmerged(m3)timesthedensity

ofwater(1000kg/m3)timesthegravitationalacceleration(9.8m/s2).

OtherThingstoTry

1. Take a weight of known volume. Either calculate the volume using geometry or determine how much water it

displaces. Measure the weight on a spring scale in the air. Immerse the weight in the water. How is the weight

affectedbybeingimmersedinwater?Howdoesthiscomparewiththeweightofthewaterthatwouldfillthevolume

ofthesubmergedobject?

2. Predicthowmuchweightaboatcansupportbasedontheweightofthewaterthatitcanhold.Testyourprediction.

3. Predictwhereafloatlinewillbebasedonthevolumecontainedbelowthefloatlinesetequaltotheweighttobe

addedtotheboat.

ThePoint

Abuoyantforceisexertedonanobjectthatisfloatingorsubmergedinaliquid.Anobjectwillfloatifitislessdensethanthe

liquiditisfloatingin.Thebuoyantforceexertedonanobjectfloatinginwaterequalstheweightofwaterthatwouldoccupy

thevolumeoftheobjectthatisunderwater.

144

Project39

Cartesiandiver.

TheIdea

Anobjectisbarelyfloatinginabottle.Inthisproject,youcontrolwhetheritfloatsorsinks,justbyapplyingpressureonthe

sideofthebottle.

WhatYouNeed

2-literplasticsodabottlewithareclosablecap

water

1medicinedropper

asmallobjectsuchasapapercliptofine-tunetheweightofthemedicinedropper

Method

1. Partiallyfillthemedicinedropperwithjustenoughwatertoestablishneutralbuoyancy,whichisaconditionwherethe

medicinedropperdoesnotsink,butalsodoesnotfloatinwater.Testandadjustuntiltherightamountofwaterisin

themedicinedropper.Usethepapercliptoincreasetheweightofthemedicinedropper.

2. Putthemedicinedropperinthesodabottle.

3. Fillthebottletothetopwithwater.

4. Capthebottlesecurely.

5. Observewhathappensasyouapplypressuretothesidesofthebottle.Whathappensasyourelievethepressure?

ExpectedResults

Whenthesideofthebottleissqueezed,thediverdescends.

Whenthepressureisreleased,thediverreturnstothesurface.

WhyItWorks

Pressureonthesideofthebottleistransmittedtothemedicinedropper.Thepressurereducesthevolumeofthemedicine

dropper.Thebuoyantforcedependsonthesizeofthemedicinedropper.Asmaller-volumemedicinedropperhasasmaller

buoyantforceandsinks.

145

Figure39-1Cartesiandiver.

With the pressure reduced, the volume of the medicine dropper increases, leading to greater buoyant force. Greater

buoyantforcecausesthemedicinedroppertorise.

Neutralbuoyancyoccurswhentheforceofgravityequalsthebuoyantforceresultinginequilibriumintheverticaldirection.

ThisisshownforaSCUBAdiverinFigure39-2.Adiverwouldaddweighttoabeltasyoudidabovewiththepaperclipto

fine-tunethebalanceofforces.

OtherThingstoTry

Onceyougetthehangofthis,youcanputa“treasure”intheformofasmallweightwithahookatthebottomofyourbottle.

Youcanthenhaveyourdivergodownandtrytorecoverthetreasure.

ThePoint

Buoyancydependsonthevolumeofasubmersedobject.Pressureexertedexternally reducesthevolumeofasubmersed

object,which,inturn,reducesthebuoyantforce.

Figure39-2Verticalforcesinequilibrium.PhotobyDr.MichaelDershowitz.

146

Project40

Anair-pressurefountain.

TheIdea

Thisisaniceattention-gettingdemonstrationthatproducesafountain-likesprayinaninvertedflask.Ifyouaredoingthisas

ademonstration—especiallyforyoungerchildren—bepreparedtobeaskedtodoitagain.

WhatYouNeed

ringstandwithasmall2-inchdiameterring

flask(250mlworks)

1-holerubberstoppertofittheflask

approximately12-inchsectionofglasstubingthatcanbeinsertedintothestopper

hotplate

ovenmitt

beakerofequalorlargervolumeastheflask

water(withfoodcoloringoptional)

safetyglasses

Method

1.Putonsafetyglasses.

2.Carefullyslidetheglasstubethroughthestopper,soapproximately1 inchprotrudesthroughthenarrowendofthe

stopper.Usepropertechniquesforhandlingtheglasstubing(includingwearingeyeprotection,protectingyourhands

as youpush it throughusinga towel, and lubricating theedgewithabit ofVaseline, so youdon’t have to force it

throughthehole).

3.Insertthestopperintotheflask.

4.Attachtheringontheringstandhighenoughsotheentirelengthofthetubingissupportedabout½inchabovethe

baseofthestand.

5.Fillthebeakerclosetothetopwithwater.(Foodcoloringcantemporarilystainyourfingers.)

6.Assembletheapparatus,asshowninFigure40-1.Makesureeverythingfitsandissecure.

147

Figure40-1Airpressurefountain.

7.Taketheflaskoutoftheringstandandremovethestopperwiththetubing.

8.Put(afewtablespoonsof)waterintotheflask.Setthestopperonatable.

9.Placetheflaskonthehotplate(Figure40-2).

10.Whenthewaterstartstoboilandtheflaskfillswithsteam(usingtheovenmitt),removetheflaskfromthehotplate

andattachthestopper.

11.Quickly,butcarefully(stillusingtheovenmitt),reassembletheapparatus.Oneconvenientwaytodothisistonote

thepositionofthering,removethering,andthenplacetheringoverthecollaroftheflask.Then,withthestopper

inserted,inverttheflask,and(withtheflasksupportedbytheringasitistransferred)reattachtheringonthestand.

Itwouldn’thurttochoreographthisalittlebitbeforedoingit(andhaveasecondpersonhelpyou).Theideaistodo

the transferquickly (soyoudon’t loseallofyoursteam),butsafely (becauseyouareworkingwithglassandhot

liquids).Placinganicecubeontopoftheflaskmayfurtheracceleratetheprocess.

148

Figure40-2Heatasmallamountofwaterintheflask.

12.Withtheflaskintheringstandandtheglasstubingclosetothebottomofthebeaker,observewhathappens.

ExpectedResults

Atfirst,thewaterstartstoriseupthetube.Thisbeginsslowlyatfirst.Asthewaterworksitswayupthetube,itbeginsto

pourintotheflask.Oncethewatertouchestheinterioroftheflask,itbeginstospray,formingafountainthatincreasesin

intensityuntilthewateriscompletelydrawnoutoftheflask(Figure40-3).

Ifpositionedjustright,thefountainendsinagurglingeffect.Whilemanyobserversmayexpecttheriseoftheliquidupthe

tube,thesurgeofthefountaincatchesmanypeopleoffguard.

149

Figure40-3Airpressurecausestheliquidtosprayintotheflask.

WhyItWorks

Asthesteaminsidetheflaskbeginstocool,theairpressureinsidetheflaskdrops.Thisisprimarilytheresultofthephase

changeofthesteamfromvaportoliquidwater,whichoccupiesamuchsmallervolume.Thecoolingairinsidetheflaskalso

contracts,addingtothereducedpressure.Atmosphericpressurepushesdownontheliquidintheflask,drivingupintothe

glass tube. The cooler the flask gets, the lower the pressure. This process feeds on itself in an accelerating manner,

producingthefountaineffect.

OtherThingstoTry

ThemechanismthatdrivestheliquidupintotheflaskisthebasisforwhatisknownasaTorricellibarometer.Airpressureis

measuredby howhigha columnofwater canbe supported byair pressurewitha vacuum in the flask.Mercury is used

insteadofwater because standardair pressure can support amercury column roughly 30 inches high, comparedwith a

much-highercolumnforwater.Becauseofpotentialdifficulties inworkingwithmercury inacademicsettings, it isprobably

bestjusttoreadaboutthisone.

ThePoint

Thisprojectworksbecauseofthevolumedifferencesbetweenvaporandliquid,andtheforceexertedbyairpressure.

150

Project41

Blowingupamarshmallow.Lessiss’more.Whyastronautsdonotuseshavingcreamin

space.

TheIdea

Thenexttimeyouaresittingaroundthecampfirecookingupabatchofs’mores,besuretopointouttoyourfriendsthata

marshmallowissimplyacolloidalsuspensionofairinasolid.Becausetheairinthemarshmallowisinequilibriumwiththe

atmosphere,thevolumeofthemarshmallowisstableatstandardairpressure.However,it’sadifferentstoryifwedisturbthe

equilibriumconditionsbytakingawaytheatmosphericpressure.

WhatYouNeed

marshmallow

belljar

vacuumpump

Method

1. Placeamarshmallowonthebaseofthebelljar.

2. Assemblethebelljarandapplyavacuum.

3. Observewhathappens.

ExpectedResults

Themarshmallowgrowsinvolume,asyoucanseeinFigure41-1.

WhyItWorks

Thepressureof theair trapped ineachmarshmallowcauses themarshmallow toexpandwhen thepressureoutside the

marshmallowisreduced.

151

Figure41-1Airpressure trapped inamarshmallowcausesexpansionof themarshmallow. (Thevacuum jarpicturedhere

wasadaptedfromanapparatususedtoshowthedropoffinsoundtransmissionasairpressureisreduced.)

OtherThingstoTry

Trythiswithshavingcream.Itwillincreaseinvolume.

Trythiswithhotwater,justundertheboilingpoint.Thewatershouldbegintoboilagain.

ThePoint

Commonobjectsdependonairpressureforthemtomaintaintheirphysicalshapeandappearance.

152

Project42

Relaxingonabedofnails.

TheIdea

Wouldyousitdownonabunchofnailsthatarestickingoutofawoodenboardwiththesharppointysidesupward?Thisis

yourchancetotry.Thisisnotnearlyaspainfulasitmayseembecausethelargenumberofnailsspreadstheforceovera

largerarea.

WhatYouNeed

144nails,1½to2incheslong.Whateverlengthyouuse,makesurethenailsarenearlyallthesamelength

pieceofplywood14inches×14inches×¾inchesthick(orlarger)electricdrill

drillbitwhosediameterisequaltoorjustslightlysmallerthanthediameterofthenails

inflatedballoon

Method

Assemblingthebed

1. Drawevenlyspacedlinesat1-inchintervalsrunningparallelwitheachoftheedgesoftheboard.

2. Drillaholeattheintersectionofeachoftheholes.

3. Insert the nails in the holes.They should be snugenough not to fall out. Somemay have to be driven inwith a

hammer(Figure42-1).

Testingthebed

1. Presstheballoonononeofthenailsonthecorner.

2. Press(another)ballooninthecenterofthebed(Figure42-2).

3. Placethenailsonachairandsitdownonit.

153

Figure42-1Bedofnails.

Figure42-2Theforceisspreadoutoveralargenumberofnails.

ExpectedResults

Withonenail isolated, theballoonwillburst.However,withseveralnails incontactwith theballoon, theballoondoesnot

burst,evenwithsubstantialpressureapplied.Sittingonthebedofnailsissurprisinglypainless.

WhyItWorks

Pressure is forcedividedbyarea.Foragiven forcepressingdownon theballoon, thepressure ismuchgreaterwith the

singlenailthanwiththelargegroupofnails.Whenyousitonthegroupofnails,theforceistheresultofyourweight,butthe

pressureisspreadoutoverthelargenumberofnails.

Razorbladesthatusemultiplebladesapplytheprincipleofspreadingouttheforceexertedbyanyonebladeoveralarge

surfacearea.

OtherThingstoTry

Insteadofjustaseat,whynotbuildanicecomfortablebedtosleepon?

Youcanalsoshowhowpressurecanbespreadoutoveralargerareabyusingseveralcupstosupportaperson.Setupa

boardonarowofpapercups,asshowninFigure42-3.Then,haveapersonstandontheboard.Ifyouhaveenoughcups,

youshouldbeabletostandontheboardsupportedbythepapercups.Somecupsarestronger thanothers,soyoumay

havetoexperimenttodeterminehowmanyyouneed.Placingthemevery2inchesorso,however,isagoodplacetostart.

154

Figure42-3Theperson’sweightisdistributedoverseveralcups.

ThePoint

Pressureisforcedividedbyarea.Thelargertheareaaforceisappliedover,thesmallerthepressureexperienced.

155

Project43

Blowinghangingcansapart.WhatBernoullihadtosayaboutthis.

TheIdea

Hereisasimplechallenge:hangtwoemptysodacansfromastring,separatedbyafewinches,andthenblowthemapart.

Whetheryouuseyourlungsorahairdryer,theresultwillbethesame.

WhatYouNeed

2emptysodacans

2strings

blowdryer

Method

1. Attachthestringstothecanandhangfromasupport(suchasaringstand).

2. With the blow dryer (or your own breath if you are good at blowing out birthday candles), direct a streamof air

betweenthecans.Avoidblowingsohardthatthecansstartbouncingaround,whichwillonlyservetoconfusethe

issue.

3. Observewhathappens(Figure43-1).

ExpectedResults

Insteadofblowingthecansapart,theairstreamwilldrivethemtogether.Infact,theharderyoublow,thegreatertheforce

thatmovesthecanstogether.

156

Figure43-1Greaterairvelocityresultsinlowerpressuretodrawcantogether.

WhyItWorks

WhatisgoingonherewasexplainedbyBernoulli.Akeyconsequenceoftheprinciplethatbearshisnameisthefasterair

moves,thelowertheairpressure.Thisisthemechanismforairplanelift.Thecontouroftheairplanewingdirectsairabove

thewingatahighervelocity,resultinginalowerpressureabovethewing.Aspoileronaracecardoesthesamething,but

upsidedown.AsailboattakesadvantageofBernoulli’sprinciplebydirectingtheair infrontofthesailatahighervelocity.

Thisproducesagreaterforceonthewingandenablesthesailboattomoveatagreatervelocitythanthewinddrivingit.

OtherThingstoTry

Astreamofmovingairfromablowdryerkeepsanobject,suchasaping-pongball,suspendedinmidair.SeeFigure43-2.

ThisisanotherexampleofBernoulli’sprinciple.Thefastermovingairinthecenterresultsinapressuregradientthatdraws

theballintotheairsteamabovetheblowdryer.

AnotherwaytoexploreBernoulli’sprincipleistotakeasheetofpaperandholdithorizontallyinfrontofyourmouth.The

paperwilldroopdowninfrontofyou.Blowingacrossthetopofthepaperwillreducethepressureabovethepaper,causing

ittodefygravityandstraightenouthorizontally.

Ifyouplaceadowelinthecenterofarolloftoiletpaperanddirectablowdryeracrossthetop,youcanrunouttheentire

roll! Ifanyonecomplainsabout themess, justsayyouhad todo it toproveBernoulli’sprinciple. (Then,ofcourse,please

157

cleanupthemess.)

Figure43-2PingpongballlevitatedbyBernoulli’sprinciple.

ThePoint

AccordingtoBernoulli’sprinciple,movingairresultsinlowerpressure.

158

Project44

Centerofmass.Howtobalanceabroom.

TheIdea

Experiencetellsusthatobjectsaremorestableiftheircenterofmassislowertotheground.Basedonthat,youmightthink

itwouldbeeasiertobalanceabroomwithbrushsidedown.Thisexperimentletsyouanswerwhetherthatisthecase.

WhatYouNeed

meterstick

2books(physicstextbooksarepreferred,butEnglishtextbooksworkalmostaswell)

ducttape

alternative:youcandothiswithanactualbroomoranyotherobjectthathasmuchofitsmassconcentratedatonly

oneend.Thiscanbedonewithmodelingclayattachedtotheendofabroomorpencil.

Figure44-1Whichiseasiertobalance?

Method

1. Insertthemeterstickbetweenthetwobooks,soaninchortwoofthemeterstickprotrudesbeyondthebottomofthe

book.

2. Securethebooktothemeterstick.

3. Predictwhichendofthemeterstickyoushouldsupporttomosteasilybalanceit:theheavyendorthelightend?

4. Supportthemeterstickontheheavyend.

5. Trythiswiththeheavyendupandthelightendsupportedbyyourhand.

ExpectedResults

Onemight say thatwith themassat thebottom, themeterstickwill bemorestable.The logic is, likewithadrag racer,

placingthecenterofgravityatthelowestpointpossibleresultsinthegreateststability.Theresultsoftryingthis,however,

159

revealtheoppositetobethecase.Itiseasiertobalancethemeterstickwiththeweightatthetop,notthebottom.

WhyItWorks

Thereasonforthisunexpectedbehavioristhatasmallmovementatthesupportendcreatesagreatertorquewithmostof

theweightlocatedattheoppositeend.Thisgivesthepersontryingtobalancethemeterstickgreatercontrol.Thisprinciple

isusedbytightropewalkerswhocarryapolewithaweightattheendtohelpestablishbalance.

OtherThingstoTry

Skyscrapersareoftensubjected tovibrationwhen they’reexposed towind.Sometimes,addingmass to thestructurecan

dampdowntheextentoftheswaying.Applytheresultsofthisinvestigationtodeterminewhetheritismoreadvantageousto

addmasstothetopfloorortothefirstfloorofaskyscraper.Lookupaspecificexampleofhowmasswasaddedtothe

top,ratherthanthebottom,oftheSearsTowerinChicago.

ThePoint

Addingmassawayfromthepivotpointincreasesthetorqueproducedattheotherend.Thisprovidesagreaterdegreeof

controltotheendwithouttheweight.

160

Project45

Asimplechallenge.Moveyourfingerstothecenterofameterstick.

TheIdea

OK.Hereisanothersimplechallenge:Getameterstick.Placeonefingernearthe15cmmarkandtheotherfingernearthe

65cmmark.Movebothfingerstogetheratapproximatelythesamevelocity,sotheymeettogetheratthe40cmmark. Is

thataskingtoomuch?

WhatYouNeed

meterstick

Method

1. Placethemeterstickhorizontallyandholdwithanoutstretchedfingerfromeachhand.

2. Placeyourfingersnearthe15and65metermarkingsofameterstick(Figure45-1).

3. Movebothfingersatroughlythesamevelocity,sotheymeetatthe40metermark.

ExpectedResults

Thisdoessoundsimpleenoughbutthisisjustaboutimpossibleformostpeopletodo.Youwillfindyoucanonlymovethe

fingerfurthestfromthecenter(theonestartingatthe15centimetermark)untilbothfingersarethesamedistancefromthe

center.Then,theymeetclosetothemiddle(the50cmmark).SeeFigure45-2.

WhyItWorks

Alotofphysicsisactuallyinthislittleinvestigation.Theforceisgreateronthefingerfurthestfromthecenter(becausethere

isgreatertorquetryingtorotatethemeterstickinthatdirection).Thegreatertheforce,thegreatertheforceoffriction.This

resultsinonefingerbeingabletomovemuchmoreeasilythantheother.

161

Figure45-1Thefingerthathasstartedonthe15cmmarkstartstomovewhilethefingeronthe65cmmarkhasn’tmoved

atall.

Figure45-2Bothfingerseventuallymeetatthe50cmline.Notthe40cmline.

OtherThingstoTry

162

Trythiswithdifferentstartingfingerpositions.Youmayalsoneedtoconvinceanyskepticsthatonesideofthemeterstick

doesnothavemorefrictionthantheother.

ThePoint

The furtheraweight is fromapivotpoint, thegreater the force itexerts.Greater forcebetween thesurfaces incontact

resultsingreaterfriction.

163

Project46

Centerofgravity.Howfarcanastackofbooksextendbeyondtheedgeofatable?

TheIdea

Youhavefourequalbooks.Eachis10incheslong.Youcanstackthemupanywayyoulike.Howfarfromtheedgeofthe

tablecanyouplacethefaredgeofthetopbook,soallfourbooksstillbalanceovertheedgeofthetable?Thiscanbe

donebyintuitionoranalytically.Italsomakesagoodcompetitionactivity.

WhatYouNeed

stackofobjects:bricks,blocks,books,oremptyCDcases

ruler

Method

1. Beforeyoustart,stateyourprediction.Howfarbeyondtheedgeofthetablewillthefourbooksgo,sotheybalance

withoutfalling?SeeFigure46-1.

2. Takethefourbooksandarrangethem,sothefourthobjectextendsasfarfromtheedgeofthetableaspossible.

3. Repeat with any other number of books. This makes a good friendly competition to see who can produce the

greatestoverhang.

ExpectedResults

Ifyouhavefoursimilarobjects,10incheslong,themaximumoverhangwillbejustunder9.4inches.Ingeneral,ifyouhave

fourobjectswhoselengthisL,themaximumoverhangis(justunder)0.94×L.

164

Figure46-1Howfarcanthebooksextendbeyondtheedgeofthetable?

WhyItWorks

Thebooks(orotherobjects)willbalanceonthetableifthecenterofmassforallthebooksliesoverthetable.Ifthecenter

ofmassispositionedovertheedgeofthetable,theentirestackofbookswilltopple.

Let’sstartwithonebook.Thebookbalanceswiththeoverhangnogreaterthanhalfway.Withasecondbookadded,the

equilibriumismaintainedwiththeaddedbookextendingone-quarterofitslengthbeyondthefirst.Asbooksareadded,the

addeddistancethattheentirestackcanbepushedoutisone-halfthelengthofthatofthepreviousbook,asindicatedin

Figure46-2.

165

Figure46-2Spacingforamaximumoverhang.

OtherThingstoTry

Nowthatyougotpastfourbooks,howabout100?Extendingthistoalargenumberofbooks,theoverhangisextendedby

thebooklengthdividedbyone-halfofthetotalnumberofbooks.

Figure46-3

Thetotaloverhangisthesumofalltheindividualextensions.Asanexample,for100books,eachofalength10inches,the

maximumoverhangwouldbe25.9inchesaspicturedinFigure46-3.

ThePoint

Equilibriumismaintainedwhenthecenterofmassiscenteredovertheareaofsupport.

166

Project47

Centerofmass.Theleaningtowerofpizza.

TheIdea

Howfarcananobjecttiltbeforeitfalls?LiketheLeaningTowerofPisa,thestabilityofarectangularorcylindricalobject

depends on its shape.This experiment establishes a simple condition for stability of an object and explores the ideaof

centerofmass.

WhatYouNeed

cerealbox

pizzabox

2pencils

tape

string

2nuts,largewashers,orothermatchedattachableweights

woodenboardtouseasanincline(roughly3ft×4inches×½inch,or1m×0.1m×0.01m)

Method

1. Findthecenterofeachoftherectangularfacesofthebox.

2. Start with the largest face first. Push one pencil through both sides of the box. The pencil should be roughly

perpendiculartothesurfaceitispushedthrough.

3. Tiethestring—oneendtothepencilandtheotherendtothehangableweight.

4. Attachtheotherweighttotheothersideofthepencilasacounterbalance.Youcanusestringifthatmakesthis

easier.

5. Tapetheotherpencilacrosstheincline,somewhereroughlynearthemidpoint.

6. Placetheboxontheincline,sothedownhillsideoftheboxisincontactwiththepenciltapedtotheincline.This

pencilservesasapivotpointtoforcetheboxtorotate,ratherthanslidedown,theincline.

7. Makeyourpredictions.Howfarcanyoulifttheinclinebeforetheboxtopples?

8. Trythiswiththevariousfacesofeachoftheboxes.Canyoudevelopageneralconditionforstability?

9. Youcandothisqualitativelyasdiscussedpreviouslyortakeitastepfurtherandrelatethegeometryoftheboxto

theangleitcantiltatandstillbestable.Canyoupredictthemaximumangleofstabilityforgivenboxdimensions?

ExpectedResults

Theboxwillbestableifthecenterofmass(markedbythepencil) isoverthebaseoftheboxincontactwiththeincline.

Oncetheangleincreasestothepointwhereitisoutsidethebase,theobjectwillrotate.

Objectsaremorestablewhenthecenterofmassisclosesttotheincline.

Becauseapizzaboxhasasquare-topface, itwillbestableuptoa45-degreeanglewhenproppedupwithoneofthe

longedgesplacedalongtheincline,asshowninFigure47-1.

167

Figure47-1Theleaningtowerof“pizza.”

IfA is the lengthof thesideof thebox incontactwith the inclineand ifB is theheightof thebox (for thatparticular

arrangement)abovethe incline, themaximumstableangle isgivenby: tangent (angle)=A/B. (Theanglecanbefoundby

takingtheinversetangentorarctan,whichcanbefoundonmostscientificcalculators.)

For instance, a 17-ounce box of Honey Nut Cherrios has dimensions 12 inches× 7¾ inches× 2¾ inches. The sixpossibleplacementsforthisboxaresummarizedinTable47-1.

AfewoftheseareillustratedinthefollowingFigures47-2,47-3,and47-4.

WhyItWorks

Massiveobjectstendtoactasifalltheirmasswasconcentratedinasinglepointcalledthecenterofmass.Gravitypulling

onthatpointcausestheboxtorotateaboutthepivotpointestablishedbythepencil.Ifthecenterofmassisabovethebase

ofsupport,theobjecttendstorotateinsuchawayastoremainstableontheincline.However,asthecenterofmassmoves

outfromabovethebase,atorqueisapplied,whichtendstorotatetheobject,soitrollsdowntheincline.

OtherThingstoTry

Thisapproachcanbeeasilyextendedtoothershapes.Youcancutacardboardtubeatananglenearthebottomedgeto

forma replicaof theLeaningTowerofPisa (notnecessarily toscale).Try tocut it insuchaway that the tube remains

standingattheminimumpossibleanglewithrespecttotheground.Thiswouldmakeafunchallengeforagroup.Thiscanbe

doneeitherby trial-and-errororbycalculationsbasedonanapproximately rectangularcross-section.By theway, thereal

LeaningTowerofPisaiscurrentlytiltedat5.6degreesandwouldtoppleifthatangleincreased1.4degrees,accordingtoa

tilt angle of 7 degrees (Rossella Lorenzi, Discovery Channel Online News www.discovery.com, September 1998,

http://www.endex.com/gf/buildings/ltpisa/ltpnews/ltpdisc092298.htm).Themassdistributionof the LeaningTowerofPisa is

notstrictlythatofacylinderandcurrentlybenefitsfromvarioustechniquesofshoringitup.

Table47-1

168

Figure47-2

169

Figure47-3

Figure47-4

Bythesametoken,youcancutcardboardmailingtubesin3″,6″,9″,and12″lengths.Then,placethemonaboardwithastoptokeepthemfromsliding.Asyoutilttheboard,eachofthetubeswilltoppleinsequence,startingwiththetallest.

170

ThePoint

Objectsarestableiftheircenterofmassiswithintheirbaseofsupport.

171

Section5

Energy/Momentum

Project48

Thependulumandyourphysicsteacher’sMingdynastyvase.

TheIdea

Energy is neither created nor destroyed; or asphysicists say, energy is always conserved.This project is a test in one’s

confidenceinthistime-honoredprinciple.Thisexperimentcanbedonewithanysizependulum.However,alargependulum

withaheavymassraisesthestakesandincreasesthesuspense.

WhatYouNeed

pendulum

–mass:consistingofanymassthatcanbesecurelysupported(suchasahookedmassorabowlingball)

–stringorcablestrongenoughtosupportthemass

–secureoverheadsupportsuchasaceilingbeamthatcansafelyhandlethemovingmass

fragile object you do not want destroyed by the pendulum. You may want to start with a plastic bottle before

attemptingthisonyourmoreexpensivepottery.

Method

1. Setupthependulum,soitswingsfreely.

2. Setanobjectinthepathofthependulum.

3. Positionthependulummass,soitisbetweentheobjectandtheequilibriumpoint,andjusttouchingthevase.

4. Release,butdon’tpushthependulummassfromitspointofcontactwiththeobject.

5. Letthependulumgothroughafullexcursionfromwhereitwasreleased,andthenback.

ExpectedResults

Ifthemasswasreleasedandnotpushed,itwillnevergohigherthanthepointfromwhichitwasreleased.Thependulumwill

returnto,butneverexceed,thereleasepoint.

For people who are still in the process of developing a sense of confidence in the law of conservation of energy, a

momentofsuspensemayexistasthependulumreturnstoitsoriginalheight.Inanyrealpendulum,thereisacertainamount

offrictioninthepointofcontactandfromairresistance.Becauseofthis,thependulumreturnstoapointslightlylowerthan

thepointfromwhichitwasreleasedfrom.

172

Figure48-1Whatgoesdown,mustcomeup(toalmostthesameheightthatitwasreleasedfrom).

WhyItWorks

Thepotentialenergyofanobjectisequaltoitsweighttimestheheightitisraisedto.Forobjectsreleasedfromrest,asis

thecasehere,thereisnostartingkineticenergy.So,theamountofpotentialenergyyoustartwithequals(orisslightlylower

than) the final kinetic energy. The pendulumwill never quite return to the level that it was released frombecause some

energyis“lostto”frictionasthemechanicalenergyistransformedintothermalenergy.

OtherThingstoTry

Avariationonthisinvolvestherelatedideaofconservationofangularmomentum.Ifyoureleaseapenduluminsuchaway

thatitdoesnothitthevase,nomatterhowmanytimesitswingsbackandforth,itwillnothitthevase.

ThePoint

Theamountofenergycontainedinamovingobject,suchasaswingingpendulum,canneitherbecreatednordestroyed.

173

Project49

Twoslopes.Differentangle,sameheight.

TheIdea

Thisexperimentcompareshowmuchenergyanobjecthasafter followingseveraldifferentpaths.Wecandeterminehow

muchenergyaballhasafterrollingdownaninclinebymeasuringhowfaritrollsoffatable.

WhatYouNeed

2inclinessupportedbyaringstandorastackofbooks(oneinclinethatworkswellwithgolfballsisavinylbullnose

sectionofmoldingavailableathomesupplystores)

2golfballsorothermatchedobjectstorolldowntheincline,suchasmarbles,coffeecans,toycars,oraairtrack

glider

meterstickortapemeasure

optional:motionsensor

Method

1.Setuptheinclinesattwodifferentslopes,asshowninFigure49-1.Allowenoughspaceatthebottomoftheincline

sothatthegolfballsrolloffthetablehorizontally.

2.Avoidananglethatissosevereastocausethegolfballstobounceontheedgeofthetable.

3.Aligntheinclinessotheyarepointinginthesamedirection.

4.Holdthetwogolfballsatequalheightabovethetable.Thismaybeeasierwithtwopeople.

174

Figure49-1

5.Predictwhatyouthinkwillhappenwitheachoftheballs.Whichwillcomedownwiththegreatestvelocity?Thevelocity

canbedeterminedeitherbyusingamotionsensororbycomparingthepointthatithitsthefloorafterrollingoffthe

table.

6.Releasebothgolfballsandcomparetheresultswithyourprediction.

ExpectedResults

Bothballsshouldmovewiththesamevelocity,astheyrollhorizontallyacrossthetable.Theballsthenhittheflooratthe

samedistancefromtheedgeofthetable.

WhyItWorks

Inthis,asinallotherprojects,energyisconserved.Theenergyeachofthetwogolfballsstartsoffwithisthesamebecause

they are released from the same height. This is equal to the object’s weight times gravitational acceleration. All of this

energyisconvertedtokineticenergy(neglectingfrictionallosses)whentheballsgettothebottomoftheincline.Withequal

kineticenergy,theobjectswillmoveatthesamevelocity.

OtherThingstoTry

Pickoneoftheslopesandholdagolfballontheinclineateachofthreedifferentplaces(forexampleat6-inchintervals

startingfromthetopoftheincline).Predicttheoutcome.Releasetheballfromeachofthethreepositionsandcomparethe

resultswithyourpredictions.Here,theballstartswiththreedifferentamountsofpotentialenergy.Itcomesofftheinclinewith

threedifferentvelocities,asshowninFigure49-2.Accordingtothe lawofconservationofenergy(neglectingfriction), the

potentialenergy(mgh)isconvertedtokineticenergy(½mv2).Thedistancethatahorizontalprojectiletravelsisproportional

toitshorizontalvelocity.Asaresult,therangeordistancealongthefloorwillgoasthesquarerootoftheheightabovethe

table.

ThePoint

Total mechanical energy (consisting of kinetic and potential energy) is conserved unless some energy is consumed in

overcomingfriction.Objectsreleasedfromthesameheighthaveequalpotentialenergy.Whenthisenergy isconvertedto

kineticenergy,thepaththeobjectsmovetowardthebottomisnotimportant.

175

Figure49-2

176

Project50

Racingballs.Thehighroadversusthelowroad.Whichwins?

TheIdea

Whichpathwilltaketheleastamountoftimeforarollingball?

apaththatisstraightandhorizontal,or

alongerpaththatstartshorizontally,dipsinacurvedpathwithoutexcessivefriction,andthenreturnstothesame

horizontallevelitstartedfrom.

Onepath isshorter.Soyoumight think itwill take the leastamountof time.Becausebothobjects return to thesame

height, theywindupwith thesameamountofenergy.Howdoes thataffect theoverall time for the journey?Figure50-1

showsthetwopaths.

WhatYouNeed

2golfballs

materialstobuildatrack:

–flexibleflatwoodenmolding—onesection8feetlongandonesection6feetlong

–asideboardabout6feetlong

–acoupleof2″×4″×6″piecestoserveasabase–smallflat-headwoodscrews

–smallwoodenormetalright-anglebraces—1inchcornermoldingwillwork

–optional—abasketorplasticcup

Thistypeofapparatusisalsocommerciallyavailable,asshowninthelaterFigures50-6and50-7.

Method

Buildingthetrack

1.Draworsketchtheshapeofthecurvedsection.Thiscanbetraced,copied,oreyeballed.Amoreexactingapproach

wouldbetogenerateageometriccycloidandformthecurveintothatshape.

2.Attach theflexible track to thesideboardwithastraightsection,adownwardcurve returning toasecondstraight

section. Attach the braces to the side board and secure the flexible track to the braces. (Keep the profile of the

screwsaslowaspossible,soitdoesnotinterferewiththemotionofthegolfball.Itmaybenecessarytocountersink

thescrewhole,sothescrewheadisbelowthelevelofthetrack.)

177

Figure50-1Bothballstartatthesameheight.CourtesyDanSilver.

3.Attachthestraightsectiontothesideboard,afewinchesabovethesectionwiththedetour.

4.Attachthebaseinsuchawaythatthepaththeballwillfollowisslightlytiltedtowardthesideboard.Thisminimizes

thefrictiontheballencounters,butitwillallowtheballtorollwithoutfallingoffthetrack.

5.Youmaywanttoaddsomewaytocatchtheballsaftereachracetoavoidhavingtochasethemeverytime.

6.Arampofequalslopeandequallengthisplacedatthestartofeachpathtogiveobjectsracingdownthetwopaths

thesamestartingvelocity.Besuretokeepanyseamsinthetrackaslowprofileaspossible.

Racing

1. Beforedoingthis,observerscanmaketheirprediction.Whichtrackisfastest:a)theflattrackb)thetrackwiththe

detourc)boththesame?

2. Release both balls from the sameheight (above the initial flat section of track) at the same time. Observe the

progressoftheballs.Repeatafewtimestomakesuretheresultsareconsistent.

Comparingenergy

Attheendofthetrack,regardlessofwhichballfinishesbeforetheother,measurethevelocityonthefinalflatsection.You

candothisinseveralways:

1. Useamotionsensortomeasurethespeedoftheballsoneachoftheflatsections.Ifyouhavetwomotionsensors,

youcanmeasurethematthesametime.Ifyouhaveone,youcandothemoneaftertheother.Ineithercase,the

mostdefinitiveconclusionwillresultfromagoodstatisticalsample.

2. Anotherwaytomeasurevelocityistotakeadvantageofthefactthattherangeofahorizontalprojectile(asyou

sawinProject6)dependsonlyon itsheightabovethegroundandthevelocitywithwhich it leavesthehorizontal

surface.IntheapparatusshowninFig50-1itisclearthatthestartingandstoppinglevelforeachofthetracksisat

adifferentheightabovetheground.Thisdoesnotaffecttheirmovementrelativetoeachother.However, itdoes

givethetrackontopanadvantagewhereitwilllandunlesstheheightdifferenceiscompensatedforbyraisingthe

landing level. If this is done, balls thatmove the samedistancealong thegroundhave the same velocity. Some

designssuchasatrackusedatMichiganStateUniversity(http://demo.pa.msu.edu/PicList.asp?DID=DID18)arebuilt

withthetwotracksside-by-side,sothisvelocitycomparisoncanbemademoreeasily.Plansforasimilarracing-ball

track are available from the University of Maryland Physics Department at

http://www.physics.umd.edu/deptinfo/facilities/lecdem/services/demos/demosc2/c2-11dwg.jpg.

ExpectedResults

Theballontheflattrackwillmovewithconstantvelocity(Figure50-2).

Theballfollowingthedetourwillincreaseitsspeed,soitisgoingfastenoughtomakeupfortheextradistance(Figure

50-3).

Oncereturningtotheoriginalheight,theballthatwentthroughthedetourwillreturntoitsoriginalspeed.However,nowit

willbeaheadoftheballontheflattrack.Theballonthedetourwillreachtheendofthetrackfirst(Figure50-4).

178

Figure50-2Bothballsbeginwiththesamevelocity.CourtesyDanSilver.

Figure50-3Theballonthe lowertrackpicksupenoughspeedtomoveaheadofthetopballdespitetheextradistance.

CourtesyDanSilver.

Figure50-4Bothballcompletetheirtripatthesamefinalvelocitybutwiththe lowerballclearly inthe lead.CourtesyDan

Silver.

WhyItWorks

Thestraightpath iseasy.Theball travelswiththesameconstantvelocity it isgivenatthestart. Itdoesnotgainor lose

energy,exceptforthe(relatively)smalllossduetofriction.

Onthestraightsectionofthecurvedpath,thesecondballtravelswiththesamevelocityasthefirst.Asitgoesdownhill,it

picksupspeed.Iftheshapeisright,theincreaseinspeedwillbemorethanenoughtocompensateforthelongerdistance.

OtherThingstoTry

In1696,JohannBernoullichallengedthemostbrilliantmindsofhisdaytosolvewhatisnowknownasthebrachistochrone

problem—basedontheGreek“brichistos”(shortest)and“chronos”(time).Basically,theproblemisthis:findthepathbetween

twopointsatdifferentlevelsthatanobjectactedononlybygravitywilltravelintheleastamountoftime.Thisissimilarto

theracingballconfigurationpreviouslydefined,except,inthiscase,theballsstartfromrestwithoutanyinitialvelocity.

Galileopreviouslyhadattemptedasolutiontothisproblem.ThepathGalileodefinedwasthecirculararcconnectingthe

twopoints.This,althoughagoodapproximation,wasnotthecorrectsolution.

The correct solution was found by five mathematicians who responded to Bernoulli’s challenge. This included, among

others,asolutionbySirIsaacNewton,whichwassubmittedinjustoneday.Thepathtakingtheshortesttimewasfoundto

beamathematicalcurveknownasacycloid.

Acycloidisdefinedbytheequationsx=r(t−sint)andy=r(1−cost),wherercanbethoughtofastheradiusofthecirclethatsweepsoutthecycloidandtistime.

An(inverted)cycloidgenerated(withr=1,tvaryingfrom0to3,andwithxvaluesasnegative) isshowninFigure50-5.

ThisisactuallysimilartoashapegeneratedbyapencilattheedgeofcircleinaSpirograph.

Althoughintheracing-ballscenario,wedohaveaslightheadstartintheformofaninitialvelocity,thecycloidcurveisa

goodapproximateminimaltimepathfrompointAtopointB.

Anextensiontothisprojectwouldbetobuildatrackthatcomparesagolfball followingacycloidcurvewithastraight

pathdown.

179

Figure50-5Curveshapegeneratedbyaninvertedcycloid.

Althoughthelargetrackismorefuntowatch,aminiversionofeitherofthesetrackscanbeassembledfromfoamboard

withatrackshapecutoutbasedontheshapeinFigure50-5andgluedtothebaseboard.Aclearplasticmodelcanalso

workandofferstheaddedadvantageofworkingwithanoverheadprojector.

A track system that can be used to study various aspects of conservation of energy can also be purchased. Two

examplesareshowninFigures50-6and50-7.

Figure50-6Horizontalracingballtrack.CourtesyPASCO.

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Figure50-7Brachistochronetrackandstraightincline.CourtesyPASCO.

ThePoint

Thepaththattakesadvantageofincreasingthevelocityduringpartofthetriptakeslesstimethanoneofconstantvelocity.

Thisprojectdemonstratesthat(asidefromfrictionallosses)energyisconserved.Asthepotentialenergyisreduced,itis

transformedintokineticenergy.Becausebothballshavereturnedtotheiroriginalheightandfinishedwiththesamevelocity,

weconfirmthatkineticenergyisconserved,regardlessofthepathtraveled.

181

Project51

Linearmomentum.Wherecanyoufindaperfect90-degreeangleinnature?

TheIdea

Canyouthinkofanythingthatformsaperfectrightangleinnature?Oneexampleofarightangleisthefractureplaneof

body-centeredcubiccrystal,suchascalcite.Thisexperimentexploresanotherexampleofanaturalrightanglethatresults

fromanelasticcollisionbetweentwoobjectsofequalmass.

WhatYouNeed

2low-frictionobjectsofequalmass.HoverPucksareexcellentforthis.Penniesonasmoothtablecanalsowork.

flat,levelsurface

protractor

2lengthsofstring

Method

1. Markthestartingpointof thefirst (stationary)puck. (Findareasonableflatplaceonthefloor toprevent thefirst

puckfromdriftingawayprematurely.)

2. Placethesecondpuckashortdistancefromthefirstone.(Dowhatworksforyou,but18inchesmaybeagood

startingpoint.Ifyouaredoingthiswithpennies,youprobablywanttoshortenthistoafewinches.)

3. Pushthesecondpuck(theshooter) towardthestationarypuck.Aimsothecollision isataglancingangle, rather

thanheadon,hittingthestationarypuckoff-centerasshowninFigure51-1.

4. Markoneormorepointsalongthepathofeachofthepucksafterthecollision.Youmayfindafewextrasetsof

handsarehelpfulhere.

5. Takeapieceofstringandplaceoneendat thecenterof thestationarypuck.Place theotheralong thepath it

traveled.

6. Placetheotherpieceofstringwithoneendalsoatthecenterofthestationarypuckandtheotheralongthepathof

thepuck.

7. Measuretheanglebetweenthetwostrings.

182

Figure51-1Apuck(movingtowardyou)abouttohitastationarypuck.

8.Getabetterstatisticalsamplebyrepeatingthisafewtimesandtakingtheaverage.Ifyourcollisionistoodirect,your

anglewillbezeroorclosetoitandshouldn’tbeincludedinyouraverage.

ExpectedResults

Theanglethetwopathsmakeshouldformarighttriangle,aspictureinFigure51-2.Oneexceptionisifthemovingpuckhits

alongthecenterlineofthestationarypuck,itmaystopandsendthestationarypuckmovingalongthesamepath.

WhyItWorks

Whentwoobjectscollide,momentum(givenbymasstimesvolume)isconserved.However,forelasticcollisions,suchasare

beingexplored here, kinetic energy is also conserved. The only way kinetic energy can be conserved is for the colliding

objectstoformaperfectrighttriangle.

Kineticenergyisgivenbyone-halfthemasstimesthevelocitysquared(or½mv2).Ifvcisthevelocityoftheshooterbefore

thecollision,andvbisthevelocityoftheshooterafterthecollision,thenvaisthevelocityofthestationaryobjectafterthe

collision.(Thereis,ofcourse,novelocityforthestationaryobjectbeforethecollisionbecauseitisstationary.)Conservation

ofenergygivesus:

Becausethemassisthesameforeachobject,thisreducesto:

ThisistheformatofthefamiliarPythagoreanformula(c2=a2+b2),whichappliesonlytorighttriangles.Figure51-3may

helpvisualize this.Because thevelocitiesmustbeconsistentwith thiscondition, theangle the twoHoverPucksmoveat

mustbearightangle.

OtherThingstoTry

Thisexperimentcanalsobedoneonapooltable.However,Ihaveyettoknowofanyoneactuallyimprovingtheirgameby

applying the laws of physics. The felt of a pool tablemay introduce enough friction to prevent the collisions from being

183

completelyelastic.Asheetoffoamboard,asshowninFigures51-4and51-5,canhelpthecollisionbesufficientlyelasticto

beat(nearly)a90-degreeangle.

Figure51-2Afterthe(nearlyelastic)collisionbothpucksmoveoffat90degrees.

Figure51-3ConservationofenergyrequiresthattheHoverPucksmoveoffatrightangles.

184

Figure51-4Thesolidballishittingthestrippedball.

Figure51-5Elasticcollisionfromobjectsofequalmass.

Whenresearchingthecollisionsofsubatomicparticles,sometimestheincomingparticlestrikesastationaryparticleofthe

samemass.Acollisionbetweenamovingprotonandastationaryprotonmeetsthesecriteria.Becausesubatomicparticles

followthelawofconservationofmomentum,thetrajectoryofthetwoequalmassparticles(absentanymagneticfields)as

theymoveoffisatacharacteristic90-degreeangle.

ThePoint

Conservationofkineticenergyforelasticcollisionsrequirestheangleformedbythecollidingobjectstobearightangle.

185

Project52

Elasticcollisions.

TheIdea

Whenoneobjectstrikesanother insuchaway that theobjectsbounceoffeachother, thecollision issaid tobeelastic.

When this happens,whatevermomentum you start offwith, you have at the end. In the case of an elastic collision, the

objectsalsomoveoffwiththesameoverallkineticenergytheystartedwith.Inthisproject,weexplorewhathappenswhen

collisionsareelastic.

WhatYouNeed

4poolballs(orhardballsorgolfballs)

trackfortheballstorollinonedimension(Thiscaneasilybesetupbytaping2metersstickstoasmoothboard)

largeball,suchasabasketball

smallerball,suchasaping-pongball

optional—aNewton’scradle,asshowninFigure52-1

Method

Oneballhittingthree

1. Placethreeballsofequalmassinthetrack.

2. Placethefourthballafewinchesawayinthetrack.

3. Rolltheball,soitcollideswiththeotherthree.(Thereareseveralotherwaystodothis,includingaNewton’scradle

orfourequalmassslidersinanairtrack.)

Bigball/smallball

1. Placethesmallballontopofthelargeball.

2. Dropbothballstogether.(Caution:dothisinaplacewhere,ifthesmallballgoesflyingoff,itwon’tbreakanything

andwon’thurtanyone. If theballs youareusingaresmallenough, youmaybeable todo this inaclearplastic

verticalguideorinalargegraduatedcylinder.)

186

Figure52-1Conservationofmomentumandkineticenergyrequiresthattwoballshittingthegroupalwayscausestwoballs

toslideout.

ExpectedResults

Oneballhittingfour

The incomingballcomestoadeadstop,asshown inFigures52-2and52-3.Theoutermoststationaryballmoves in the

samedirectionandatthesamevelocityastheincomingball.Theotherthreestationaryballsdonotmove.

Bigball/smallball

Theballsbouncetogether.Afterstrikingtheground,thesmallerballfliesoffwithmuchgreatervelocitythanthelargeball.

WhyItWorks

Withthestackofballs,itisnothardtounderstandhowthemomentumoftheincomingballistransferredtotheballthatgets

knockedoutofthestack.Thisisaclearillustrationofconservationoflinearmomentum.

Butwhyisonlyoneballknockedoutofthestack?Why,forinstance,doweneverhavetwoballsknockedoutwitheach

takingonehalfofthemomentumoftheincomingball?Thatwouldalsobeperfectlyconsistentwiththelawofconservation

ofmomentum. The problem is these collisions are elastic collisions, whichmeans not only ismomentum conserved, but

kineticenergyisalsoconserved.Theonlywaythiscanhappenisforasingleballtoemergefromthestackwiththesame

momentumastheincomingball.

Withthelargeandsmallballs,thelargeballhavingalargermassconservesmomentumbycausingthesmallerballwitha

lowermasstoflyoffwithalargervelocity.

OtherThingstoTry

ANewton’scradle,asshowninthepreviousFigure52-1,isanothergoodwaytostudyelasticcollisions.InaNewton’scradle,

twoballsneverreboundwhenstruckbyasingleballandthreeballsneverreboundwhenstruckbytwoballs.Thisistheresult

ofbothconservationoflinearmomentumandconservationofenergy.

187

Figure52-2Oneballhittingthegroup—beforecollision.CourtesyDanSilver.

Figure52-3Aftercollision—resultsinonlyoneballknockedout.CourtesyDanSilver.

ThePoint

Inanelasticcollision,bothlinearmomentumandkineticenergyareconserved.

Whenmomentumistransferredfromoneobjecttoanother,alargervelocitycompensatesforasmallermass.Inthecase

ofanelasticcollisionbetweenobjectsofequalmass,thisconditioncanbemetonlywhenthesamenumberofballsmove

afterthecollisionasweremovingbefore.

188

Project53

Inelasticcollision.Stickingtogether.

TheIdea

Whenobjectscollide,theyeitherbounceoffeachotherortheysticktogether.

WhatYouNeed

2low-frictioncarts

Velcroorducttape

low-frictiontrack(optional)

motionsensor

indexcard

tape

Method

1. Measurethemassofeachofthetwocarts.

2. AttachVelcrototheendofeachofthecarts,sowhentheymeet,theysticktogether.Youcouldalsouseducttape

formedintoaloopandattachedsticky-sideouttoeachofthecarts.

3. Setupthemotionsensoratoneendofthetable.

4. Placethefirstcartnearthemotionsensor.TheVelcrosideshouldbeinfront,awayfromthemotionsensor.Ifyou

havealow-frictiontrack,placethecartonthetrackinalinepointingawayfromthemotionsensor.

5. PlacethesecondcartnearthemidpointofthetablewiththeVelcrointherear.

6. Itmaybehelpfultoattachanindexcardtothebackofthefirstcarttomakeiteasierforthemotionsensortopick

itup.Ifyoucangetawaywithoutdoingthis,youcanavoidairresistancethatcouldslightlyaffectyourresult.

7. Setupthemotionsensortoreaddistanceandvelocityversustime.

8. Startthemotionsensor.Itshouldbeonthecartsettingandfocusedonthecardofthefirstcart.

9. Givethefirstcartapushinthedirectionofthesecondcart.Itshouldbeslowenoughtogetagoodreadingfromthe

motionsensor,butfastenoughtorear-endthesecondcartandpushitalongforatleastafewsecondsormore.

Thefirstcartcollideswiththesecondtotallyinelastically,whichmeanstheysticktogetherafterthecollision.

10. Whenbothcartsstopmoving,stopcollectingdatafromthemotionsensor.

11. Fromthemotion-sensorgraphs,findthevelocityofthefirstcartbeforethecollisionandthevelocityofbothcarts

joinedtogetherafterthecollision.Thegraphofvelocityversustimemaybealittleerraticrightafterthecollision,

reflectingtheimpact.Pickapointwherethevelocityhassettleddown.

12. Momentumisdefinedasmasstimesvelocity.Comparethemomentumbeforeandafterthecollision.

13. Kineticenergyisdefinedas½timesthemasstimesthevelocitysquared.Comparethekineticenergybeforeand

thekineticenergyafterthecollision.

Figure53-1Inelasticcollisionwithoneorbothcartsinitiallymoving.CourtesyPASCO.

189

The experimental setup is shown in Figure 53-1. (This actually shows a motion sensor at both ends. The previous

procedureusesonlyonemotionsensor,butthiscaneasilyextendedtoincludebothcarts inmotion.Forsimplicity,wewill

startoutwithoneofthecartsstationary.)

ExpectedResults

Themomentumofbothcartsbeforethecollisionshouldequalthemomentumofbothcartsafterthecollision.

Beforethecollision,oneofthecartsisstationary,whichmeansithasnomomentum,sothemovingcartistheonlyone

withmomentumbeforethecollision.

After thecollision,bothcartsstick togetherandmoveoffwith thesamevelocity.Thecombinedmassof the twocarts

togethertimestheircombinedvelocityisthemomentumafterthecollision.

Figure53-2showsthepositionversusthetimegraphbeforeandafterthecollisionobtainedbyamotionsensor.Notice

howtheslopeofthelineabruptlydrops,indicatingthecollision.

Figure53-3 shows the velocity versus time graph before and after the collision. The velocity before and after can be

determineddirectly from thegraph. You can noticea slight downward slope indicating someslowingof the carts due to

friction.Thisisnotashowstopperfortheexperiment,butitshowstheextenttowhichanairtrackcanimprovetheoverall

results.

Themostreliablevelocitymeasurementisimmediatelybeforethecollision.Thecollisionshowssomebouncingaroundand

variabilityinthevelocityforashortperioduntilthetwocartssticktogetherandmoveasone.Thisprovidessomeinsightinto

the nature of inelastic collisions, which result in the loss of kinetic energy (but not linearmomentum). Themost reliable

postcollisionvelocitytouseisthepointwhereanewhorizontallinebegins.Theresultsshouldbefairlyaccurate,butsome

lossesduetofrictionmaybeencounteredwithoutanairtrack.Also,excessivemasscanloaddownthewheelbearingand

increasethelossestofriction.

Figure53-2Motion sensor measurement of distance versus time for an inelastic collision between a moving car and a

stationarycart.

Figure 53-3 Motion sensor measurement of velocity versus time for an inelastic collision between a moving car and a

190

stationarycart.

WhyItWorks

Thetotalmomentumbeforeaninelasticcollisionequalsthetotalmomentumafter.

However,unlikeanelasticcollision,thekineticenergyforaninelasticcollisionislessafterthecollision.

OtherThingstoTry

1. Ifyouhavetwomotionsensors,youcanrepeatthiswithbothcarts initially inmotion.Youcangetthevelocityof

eachcartrightbeforethecartscollideandthevelocityofbothcartstogetherafterthecollision.Bothsensorswill

readapositivevelocitybeforethecollisionasthedistancefromthesensorincreases.Afterthecollision,onesensor

readsapositivevelocity,whiletheotherreadsanegativevelocity.ResultsareshowninFigure53-4.

2. Compare elastic and inelastic collisions using so-called “happy/sad” balls. The balls appear to be completely

identical.However,oneiselasticandbouncesbackfromthefloor,whiletheotherisinelasticanddoesn’tbounceat

all.

3. Hangelasticandinelasticballstoformapendulum.Standupawoodenblockinfrontofthependulum.Swingthe

inelasticballfirst,soitdoesn’tquiteknocktheblockover.Comparethattowhathappenswiththeelasticballswung

underthesameconditions.Elasticcollisionsresultindoublethechangeinmomentumasaninelasticcollisionunder

thesameconditions.Thisisbecauseintheelasticcollision,themomentumnotonlystops(asitdoesinthecaseof

aninelasticcollision),butitalsoreversesitselfintheotherdirection.

ThePoint

In an elastic collision, the objects bounce off each other in such as way that linear momentum and kinetic energy are

conserved.Thisistruetotheextentthatnoexternalforceoccursduringthecollision.

Inaninelasticcollision,theobjectsinteractinsuchawaythatlinearmomentumisconserved(aslongasnoforcesaffect

thecollision).However,kineticenergyisnotconservedinaninelasticcollision. Inaperfectly inelasticcollision,theobjects

sticktogetherandmoveafterthecollisionasiftheywereasingleobject.

Figure53-4 Motion sensor measurement of velocity versus time for an inelastic collision between a moving cart and a

secondmovingcart.

191

Project54

Impulseandmomentum.Eggstremephysics.

TheIdea

Whatdoyouthinkwillhappenifyouthrowaraweggashardasyoucanatablanketheldvertically?Thereisreallyonlyone

waytofindout.Thisexperimentgivesyouanopportunitytoexploretherelationshipbetweenmomentumandimpulse.

WhatYouNeed

1rawegg

blanket

3people

mopandpapertowelsforcleanup(veryoptional)

Method

1. Hold the blanket vertically, with the bottom edge curled out to form an overhang, as shown in Figure 54-1. This

requiresatleasttwopeople.

Figure54-1Throwingaraweggatablanket.

2.Thethirdpersonthrowstheeggattheblanket.Don’tholdback.Giveitagoodshot.Youcanthrowashardasyoucan

withouthavingtheeggbreakinyourhandsasyouthrow.

ExpectedResults

Youknowwhatwillhappenifyouthrowaraweggagainstacinder-blockwall.However,iftheeggisstoppedbytheblanket,

thedecelerationoccursoverasufficientlylongtime,whichpreventstheeggfrombreaking.

WhyItWorks

Momentumischangedbyaforceexertedovertime.Theabilitytochangeanobject’smomentumiscalledimpulse,whichis

definedastheforceexertedmultipliedbythetime.Anytimeanobjectisbroughttorest,thechangeinmomentumequalsthe

momentumtheobjecthadtostart,appliedintheoppositedirection.Theimpulsetobringthatobjecttorestcancomefrom

anycombinationofforceandtime,whichwhenmultiplied,equalthemomentumchange.

Iftheobject’smomentumchangesinashorttime,whichwouldoccurifaneggisthrownatacinderblockwall,theforceis

192

greater.However,iftheeggisthrownatablanketthatbringstheeggtoastopoveramuchlongerperiodoftime,theforce

ismuchsmaller.Thisiswhytheeggdoesnotbreakwhenit’sthrow,atablanket.

OtherThingstoTry

CheckouttheESPNvideoRelaxingwithMomentumthatshowswhathappensifyoudropawatermelonfromadivingboard

ontoconcrete,comparedwithdroppingawatermelonintothewater.

ThePoint

Themomentum to stopanegg thrownagainstawall andablanket is the same. However, the force in the case of the

blanketisspreadoveragreatertimeandismuchsmaller.

193

Project55

Usinggravitytomoveacar.

TheIdea

Energycanneitherbecreatednordestroyed.Oneformofenergy,however,canbechangedintoanotherformofenergy.For

instance,thecombustionthatoccursinacarengineproducesheatenergy,which,inturn,isconvertedtomechanicalmotion

bythemotor.Inthisproject,youconvertgravitationalpotentialenergyintomechanicalenergy.

WhatYouNeed

wheels:oldCDsorDVDs

posttoholdtheweight:adowel1minlengthand½to1inchindiameter

1kgweight

string

axles(dowelsworkwell)

materialstobuildthebodyofthecar

plumbingfittingorablockofwoodtoattachtheposttothecarbody

tapemeasure

stopwatch

Method

1.Assemblethecar.UseFigure55-1asaguide,butfeelfreetodevelopandbuildyourownconcept.

2.Thebasicdesigncriteriaforthecarincludes:

–TheCD(orequivalent)usedforwheelsshouldturnfreely.

–Thedescendingmassshouldfreelyturnanaxletoproduceforwardmotionofthecar.

–Thecarshouldbebalancedwiththemassinbothelevatedandfallingpositions.(Remember,a1kgmassraised1

meterabovethegroundcanexertalotoftorquethatcouldtopplethecar.)

–Themassshouldfallontothecarafteritdescends(ratherthandraggingalongtheground,whichcanlimithowfarit

goes).

–Thereshouldbeenoughsymmetrybetweenleftandright,sothecarmovesforward,ratherthanturning.

194

Figure55-1Kilogramcar.

3.Wrapthestringaroundoneoftheaxlesandattachtheotherendtotheweight.Decideifyouwantfront-wheelorrear-

wheeldriveandwrapaccordingly.

4.“Arm”thecarbyraisingthemassandleavingsomeofstringstillwrappedaroundtheaxleitwillturn.

5.Orientthecaronadesignatedcourse,andthenreleasethemass.

6.Measurehowfaritgoes.

7.Ifseveralindividualsorgroupsareinvolved,itmaybefuntodothisasaracetoseewhichcargoesthefarthestor

whichcarcrossesthefinishlinefirst.

ExpectedResults

Itmighttakeafewhourstobuildthecar(s),dependingonwhatmaterialsareavailable.Ifbuiltcorrectly,thecarshouldmove

asthemassdescends.Oncethemassfallsandcomestorest(somewhereonthecar),thecarhasenoughmomentumto

keepmoving.

WhyItWorks

Amassataheightcontributesanamountofenergyequaltoitsmasstimestheheightabovethegroundtimesgravitational

acceleration. Inthiscase,1kgdroppingadistanceof1meterwillcontribute9.8 joulesofenergy. (One joule isaboutthe

amountofenergyneededtoliftanapple1meter.)

OtherThingstoTry

Avariationof this is touseamousetraptosupply theenergy.Themousetrap isstarted in theopenposition.Aswiththe

previouskilogramcar,thepotentialenergystoredinthespringofthemousetrapistransferredtotheforwardmotionofthe

car.

ThePoint

Energyisconserved.Thepotentialenergyyoustartwithequalsthekineticenergygiventothecar(plusanyenergylostto

friction).

195

Project56

HowcanCSImeasuremuzzlevelocity?Theballisticpendulum.

TheIdea

Youcantellhowfastanobject,suchasabullet,ismovingbyhowitaffectsthemomentumofanotherobject.

WhatYouNeed

projectileandlauncher:

–golfballandaramp

–precisionprojectilelauncher

–hand-thrownhardballorgolfball

balancetomeasuremass

box

tape

string

ringstandorimprovisedsupport

protractor

meterstick

Method

1.Build(orbuy)areceiverboxthatmeetsthefollowingconditions:

–Themovingprojectileshouldbecaughtandretainedinthebox.Liningtheinteriorwithdouble-sidedducttapeorfoam

rubbercanservetocapturetheprojectile.

–Theboxissuspendedfromtheringstand.

2.Suspendtheboxfromtheringstandusingthestring.

Determinethemassoftheprojectile.

Determinethemassofthecatcherboxandincludeanyofitscontents.

Directtheprojectiletowardthecatcherboxandallowtheboxwiththeprojectilecaughtinsidetoswingupward.

Measure the maximum height above the initial starting position that the catcher box and the projectile reach.

(Alternatively,theangleandradiusofthependulumformedbythesupportedcatcherboxcanberecorded.)

ThebasicdesignoftheapparatusisshowninFigure56-1.

Thevelocityoftheprojectilecanbedeterminedfromthefollowingequation:

wheremisthemassoftheprojectile,Misthemassofthe“catcherbox,”gisthegravitationalconstant=9.8m/s2,andhis

theheightthatthecatcherboxisliftedbythemomentumoftheprojectile.

196

Figure56-1Ballisticpendulum.

ExpectedResults

Themoremomentum theprojectilehas, thegreater theangle thependulumswings through.Foragivenmass,agreater

velocitycausesagreaterprojectile.

WhyItWorks

Themomentumoftheprojectile(“bullet”)istransferredtothebox.Thegreaterthemomentumoftheprojectile,thehigherthe

boxisdriven.

OtherThingstoTry

Asemiqualitativeversionofthisconsistsofplacingacardboardboxfilledwithtissuepaperonthefloorandcomparingthe

distanceitmoveswithballsrolledorthrownintoitatdifferentspeeds.Thiscanberefinedbymeasuringthecoefficientof

kineticfrictionbetweentheboxandthefloorandthedistancetheboxslidesalongthefloor.Useoftheequationsofmotion

canbesolvedtodeterminetheinitialvelocityofthebox.

Variousballisticpendulumdesignsarealsoavailablefromsciencesupplycompanies.

ThePoint

Thevelocityofamovingobjectcanbedeterminedbymeasuringitseffectaftercollidingwithanotherobjectofknownmass.

Theballisticpendulumisbasedonconservationofmomentumappliedtoapendulum.Thelargerthevelocityoftheincoming

object,thehigherthependulumswings.

197

Project57

Angularmomentum.Ridingabike.

TheIdea

Abicycleisunstablewhenitisstationary.Ifyoutrytobalanceabikethatisnotmoving,itwillfall.Thisexperimentexplores

howitispossibletodefygravityandrideabike.

WhatYouNeed

rope—aboutameter(aboutayard)inlength

bicycletire

dowelorsectionofbroomhandletofitsnugglyintotheaxleofthetire

Method

1. Attachtheropetotheaxleofthebicycletire.Thetireshouldbeabletoturnfreelyaroundtheattachmentpoint.If

thereisnoaxle,insertacylindricalpieceofmetaloradowelforthetiretorotatearound.

2. Suspendthetirefromtherope,soittanglesfreely.Eitherholdtheotherendoftheropeinyourhandorattachitto

somethingoverhead.

3. Holdingthetireverticallybytheaxle,spinthetire.

4. Withthetirespinning,releasethetire,soitissupportedbytherope.

5. Trythiswiththetirespinningrapidlyandslowly,asshowninFigure57-1.

ExpectedResults

Thefirstthingtonoticeisthetirewillremaininclosetotheverticalposition.Also,itdoesn’ttakemuchofaspintokeepthe

tire stable. You should also be able to observe that if left alonewith the tire near the vertical position, the spinning tire

rotatesaboutthepivotpointestablishedbytherope.Thisiscalledprecession.

198

Figure57-1Itiseasyforaspinningbicyclewheeltoremainvertical.CourtesyPASCO.

WhyItWorks

Afullexplanationofthissimplesituationcangetcomplicatedinahurry.Thebasicideaisthataspinningtirehasangular

momentum.Gravity tries to rotate the tire from the vertical position that it is spinning in to the horizontal position that a

nonrotatingtirewouldbein.Theforceexertedbygravityproducesatorquethatisatrightanglestoboththeforceexerted

bygravityandthedirectionoftheangularmomentum,whichisalongthelineoftheaxle.Thisnotonlykeepsthewheelfrom

falling,butitalsocausesittoprecessinacircle.Thisformsthebasisforgyroscopicmovement.

OtherThingstoTry

Likeabicycle,atoygyroscopebecomesstableonlywhenithassufficientangularmomentumtocounterbalancethepullof

gravity.Asanextension,studyagyroscope.Observewhathappenswhenitsturningaxisisdisplacedfromastableposition.

Whataffectstherateofprecession?

ThePoint

Abicycletireisstablewhenitisrotatingbecausethetirehasangularmomentum.ThegravitationalattractionoftheEarth

exertsaforcethatwouldpullthetiretoahorizontalpositionwereitnotfortheangularmomentumofthespinningtire.The

interactionofthetorquecausedbygravityandtheangularmomentumofthespinningtireresultsintheprecessionofthetire

aboutthepivotpoint.

199

Project58

Momentofinertia.Iceskatersanddumbbells.

TheIdea

How do ice skaters get spinning so rapidly?Where do they suddenly get the energy? Are they violating conservation of

energy?Thisprojectexploreshowthisworks.Theterm“dumbbells”shouldinnowaybeconstruedtorefertotheskatersor

theexperimenters(orthewriterofthisbookforthatmatter).Theyrefertoactualdumbbells.

WhatYouNeed

(low-friction)rotatingstool

2masses,suchasapairofdumbbells(5kgorgreater)

1person

bicycletiremountedonanaxle

Method

1. Sitonthestoolwhileholdingthetwomasses.

2. Whilesittingandbalancingonthestool,rotatebypushingoffwithyourfeetorbybeingpushedbysomeoneelse.

3. Liftbothfeetfromthefloor.

4. Startwithbothmassesextendedoutatarm’slength.Then,bringtheminclosetoyourbody,asshowninFigure58-

1.

ExpectedResults

Extendingyourarmsslowsyoudown;bringingthemclosertoyourbodyletsyouspeedup.Therotationalspeed(orangular

velocity)isgreaterwhenthemassesareclosesttothecenterofrotation.Thisworksbestifthestoolrotatesveryfreelywith

aminimumof friction. The stool can be picked upat a yard sale or purchased commercially. There is also usually less

frictionforalower-massperson.

200

Figure58-1Pullinginyourarmscausesyoutospinfaster.CourtesyPASCO.

WhyItWorks

Thisprojectisanillustrationoftheprincipleofconservationofangularmomentum.Angularmomentumforarotatingmass

increaseseitheriftheobjectrotatesfasterorifthereismoremassatagreaterdistancefromthecenterofrotation.Ifthe

mass is moved further from the center of rotation, the angular velocity must increase to keep the angular momentum

constant.

OtherThingstoTry

Spinningabucketonarope

1. Sitonthestoolwithbothfeetoffthefloor.

2. Swingthebucketinacircularpathparalleltothefloor.

3. Observetheeffectofswingingfasterandslower.

4. Observetheeffectofusinglongerorshorterlengthsofrope.

Themainthingyounoticeisyourotateintheoppositedirectionthatthebucketisswung.Thefasterthebucketrotatesina

clockwisedirection,thefasteryourotateinthecounterclockwisedirection.Alongersectionofropeturnsyoufasterthana

shortersection.

ThePoint

201

Aspinningobject,suchasaskater,mustconserveangularmomentum.Amovementofmassclosertothecenterofrotation

iscompensatedbyanincreaseinhowfasttheskaterrotates.

202

Project59

WhatcausedVoyagertopointinthewrongdirection?

TheIdea

TheVoyager programproduced someof themost remarkable spacecraft ever built, providing an unprecedented viewof

nearlyeveryplanet in the solar system.AsVoyager II approached theplanetUranus, thespacecraft precisely trained its

instrumentson thatplanet’ssurface to takeadvantageof theshortwindowofopportunity togethigh-resolution,close-up

pictures.Justasthereel-to-reeltaperecorderonthespacecraftturnedontocapturethishistoricmoment,theorientationof

thespacecraftwasthrownoutofwhackandthenavigationalsystemhadtocompensatewithlast-minutecorrections.This

projecthelpsyouinvestigatewhythiscouldhavehappened.

WhatYouNeed

freelyrotatingstool

bicycletirewithhandles(themoremassivethebetter)

2people

Method:

1. Sitontherotatingstoolasbefore.

2. Havesomeonehandyouthebicycletirethathadpreviouslybeensetintomotion.SeeFigure59-1.

3. Startwiththetireinahorizontalposition.

4. Withthetirerotating,turnthetireupsidedown(soitisnowspinningintheoppositedirection).

5. Waitafewseconds.Then,turnthetireupsidedownagain.

ExpectedResults

Youwillrotateonthestoolintheoppositedirectionfromwhichthetireisrotating.Whilechangingthepositionofthetire,you

willfeelasurprisinglystrongforce,asifyouwerepushingagainstasolidwall(Figure59-2).

WhyItWorks

Startingfromrest,boththepersonandthestoolhavezeroangularmomentum.Forangularmomentumtobeconserved,itis

necessary that the person on the stool rotate in the opposite direction as the rotation of the tire to preserve angular

momentum.Whenthereel-to-reeltaperecorderonVoyagerIIturnedontorecordthespectacularimagesofUranusforthe

first time in history, it began turning with a new angular momentum. See Figure59-3. Just like the person on the stool,

Voyagerbegantoturnintheoppositedirectionasthetaperecordertoconserveangularmomentum.

203

Figure59-1Arotatingwheelhasangularmomentum.CourtesyPASCO.

Figure59-2Angularmomentumisconserved.CourtesyPASCO.

OtherThingstoTry

Thisprincipleisdemonstratedbyatoytrainrunningonacirculartrack.Thetrackismountedonaplatformattachedtoa

freelyrotatingsupport.Asthetrainmovesinonedirection,theplatformrotatesintheoppositedirectiontoconserveangular

momentum.

Figure59-3Conservationof angularmomentum requiredapositioning correctionaboardVoyager II to compensate for a

rotatingreel-to-reeltaperecorder.SourceNASA.

204

ThePoint

Angularmomentumisconserved.Thisappliestothecasewhereasystemstartswithzeroangularmomentum.

205

Project60

Momentofinertia.Thegreatsoupcanraceorthat’showIroll.

TheIdea

Iftwoidenticalcansarereleasedfromresttorolldownaninclineatthesametime,willthetopcancatchupwiththebottom

can?Doesitmatterwhatthecontentsofthecansare?Thisprojectdealswithhowthingsroll.

WhatYouNeed

2cansofthicksoup(suchasmushroomsoup)

1canofthinsoup(suchaschickenbroth)

incline

Method

Part1

1. Verifythattheexternalshapeofeachofthethreecansisthesame.

2. Setupaninclineabout1meterinlength.Theheightshouldbeabout30cm.

3. Hold the twocansofmushroomsoupon the inclinewithadistanceofabout10cmbetween them,asshown in

Figure60-1.CallthetopcanAandthebottomcanB.

4. Predictwhatwillhappenwhen thecansare released:a) thedistancebetween themwill increaseb) thedistance

betweenthemwilldecreasec)thedistancebetweenthemwillremainthesame.

Part2

1. Placeoneofthemushroomsoupcans(A)andthecanofbroth(C)ontheinclinewithA10cmhigherthanC.

2. Predictwhatwillhappenwhenthecansarereleased:sameoptionsasnumber4.

3. TrythisagainwithcanCastheuppercanthistime.

ExpectedResults

The twocanswith thesamecontentswill accelerateat thesame rate.Becausebothcansstart from rest, thedistance

between them remains constant. However, themushroom soup has a greater density than the broth and it will rollmore

slowly.

206

Figure60-1Howwillthedistance,d,changeasthecanrolldowntheslope?

WhyItWorks

Whenanobjectrolls,someofitsenergyisassociatedwithmovingfromonepointtoanother(calledtranslation).Themore

mass theobjecthasand the faster itgoes, themoreenergy ithas. Inaddition,someof theenergyofa rollingobject is

relatedtothefactthatitisrolling.Theamountofthisrotationalenergyisrelatedtothewaythemassisdistributedaround

thecenterofrotation.Agreaterdensitycenter(mushroomsoup)requiresmoreenergytorollatthesamerateasalower

densitycenter(broth).

Physicsalert:Apropertycalledmomentofinertiameasureshowmassisdistributedaroundacenterofrotation.Acanof

densesouphasagreatermomentofinertiathanacanofthinsoupand,asaresult,tiesupmoreenergyasitrolls.

OtherThingstoTry

Aninterestingfollow-upwouldbetodropbothtypesofsoupcansfromadistanceandreestablishtheprinciplethattheyboth

accelerateatthesamerateinfree-fall.Translation(falling)isdifferentthanrolling.Theeffectofrollingmakesthedifference

hereandgivestheless-densesouptheadvantage.

ThePoint

Aforceappliedtoacylindricalobjectcancauseiteithertotranslateorrotateorsomecombinationofboth.

207

Project61

Makingwaves.IthoughtInodethis.

TheIdea

Many of the things physics dealswith arewaves. This includes sound, light, and vibrations inmatter. It is helpful to use

vibratingobjects,suchaswedointhisproject,tohelpvisualizemoreabstractwaves,suchaselectromagneticwaves,which

includelight.

WhatYouNeed

slinky

coiledspring“snakey”

string

stopwatch

tapemeasure

short,thin,metalpoleorwoodendowel(10cminlengthand2mmindiametershouldworkwell)

Method

Forthefollowing,becarefulwhenworkingwithstretchedsprings.Becarefulnottoletthespringgoaccidentally,whichcould

causethespringtowhiparoundandpossiblyhitsomeone.

Longitudinalwavewithaslinky

1. Stretchtheslinkytoaboutdoubleortripleitsoriginallength.Thisrequirestwopeople.

2. Measurethedistancebetweenthetwoendsoftheslinky.

3. Fromoneoftheends,pullbackontheslinkyinthedirectionthattheslinkyisstretchedbyafewinchesandrelease.

4. Observe the pulsemoving from one end of the slinky to the other. Time how long it takes to go themeasured

distancefromoneendtotheother.

5. Calculate thevelocityof thepulsebydividing thedistance thewave travelsby the time it takes. (Useconsistent

units,meaningifyoumeasurethedistanceinmeters,thevelocitywillbeinmeterspersecond.Ifyoumeasurethe

distanceininches,thevelocitywillbeininchespersecond.)

6. Increasethetensionandcalculatethevelocity.

7. Decreasethetensionandcalculatethevelocity.

Transversewavewithacoiledspring

1. Stretchthesnakey(coilspring)toaboutdoubleortripleitsoriginallength.

2. Measurethedistancebetweenthetwoendsofthespring.

3. Fromoneoftheends,displacethecoilalongthefloorperpendiculartoitslengthbyafewinchesandrelease.

4. Measurethevelocityofthepulsewithincreasedanddecreasedtensionasintheprevioussection.

Reflectionfromfixedandunconstrainedends

208

1. Workingwiththecoiledspring,releaseatransversepulsedownthespring.

2. Bothendsofthespringshouldbeheldtight.

3. Observewhathappenstothepulsewhenitreachestheendheldtightlyinplace.

4. Now,insertthedowelorametalrodthroughoneoftheendsofthecoil.Thedowelshouldpassthroughoneora

fewcoilsinsuchawaythatthecoilisabletoslidefreelyonthedowel.

5. Againreleaseatransversepulsedownthespringandobservewhathappenswhenthepulsereachestheend.

Wavescrossingintodifferentmedia

1. Connecttheslinkyandthecoiledspringtogetherwithastring.

2. Observewhathappenstoapulsesentfromtheslinkyside.

3. Nowseewhathappenstoapulsesentfromthecoiledspringside.

4. Inwhichsection(slinkyorcoiledspring)doesthepulsemovefastest?Ifyourspringsarelongenough,timeitand

calculate the velocity. With everything else equal, a less-tense spring gives you a little more time to make the

measurement.

Superposition—constructiveanddestructiveinterference

1. Placeacoilonthefloor.Holdthecoilfrombothendsusingtwopeople—oneoneitherside.Stretchitfairlytight.

2. Eachpersonholdingthecoilsimultaneouslyshouldreleaseapulsethesamesizefromthesamesideofthecoil.

Observewhathappens.

3. Peopleholdingthecoilshouldnowreleaseapulsethesamesizefromtheoppositesidesofthecoil.Howdoesthis

comparewiththepulsereleasedfromthesameside?

Standingwavesandnodes

1. Placeacoilonthefloor.Holdthecoilfrombothendsusingtwopeople—oneoneitherside.Applymoderatetension.

2. Onepersonshouldholdtheendofthecoilstationary.

3. Theotherpersonshouldbeginshakingthecoil,slowlyatfirst.

4. Observewhathappens,foragiventension,asyouincreasethefrequencyofthevibrations.Anodeisapointonthe

wavethatdoesnotmovewhilethewavevibrates.SeeFigure61-1.

5. Quantifythisbycountingthenumberofnodesasafunctionofthefrequencyofthevibration.Thefrequencycanbe

determinedbythenumberofsecondsittakesfortenvibrations(backandforth)dividedbyten.

6. Observewhathappensasyouincreasethetensioninthecoil.

ExpectedResults

Longitudinalwave

Thevelocityofalongitudinalwaveincreasesasthetensionincreases,butisnotdependentontheamplitude.

209

Figure61-1Transversewave.

Transversewave

Similarly,thevelocityofatravelingwaveincreasesastensionincreases.

Reflection

Whenawavecomestotheendofthespringthatisrigidlyheld,thewavereflectsbyflippingovertotheoppositeside.Ifthe

springisfreetomove,thewavereflects,butbeginsitsreturnonthesamesideitcamefrom.

Differentmedia

Whenawavegoesfromonespringtoanother,thewaveispartiallyreflectedandpartiallytransmittedintothesecondspring.

Superposition

Pulses coming from the same sideof the coil add together to forma larger combined pulse.This is called constructive

interference.

Pulsescomingfromtheoppositesideofthecoilnegateeachother,resultinginasmallerpulseatthepointorevenno

pulse.Thisiscalleddestructiveinterference.

Aftercombining,theoriginalpulsescontinuemovingthroughthespring.

Standingwaves

Thegreaterthetensionandthemorerapidlythespringisshaken,thegreaterthenumberofnodesformed.

WhyItWorks

Wavesexhibit characteristic properties that include: travelingwaves, standingwaves, reflection,movingbetweendifferent

210

media,superposition,andinterference.

OtherThingstoTry

1. Standingwavescanalsobeshownby vibrating (or rotating)a string held under tensionby two vertical supports.

Wavescanbegeneratedbyamotororaspeaker,aspictureinFigure61-2.

2. Afunwaytodosomeoftheseinvestigationsistouseglow-in-the-darkropeavailablefromPASCO.

3. A significant, but often overlooked, point is the connection between the frequency of the traveling waves and

standingwaves inacoil.Theyshouldbe thesame,and thepreviously techniquesdevelopedareagoodway to

verifythis.Astandingwaveisreallyamixtureofmanystandingwavestravelingbackandforthalongthecoil.The

overall standingwavepattern isgeneratedby the travelingwaves interferingconstructivelyanddestructively.The

relationship between standing waves and traveling waves is used when measuring the speed of sound by

determiningthewavelengthofaresonantstandingwave.Thisworksbecausethespeedofbothisthesame.

ThePoint

Thepropertiesofwaves,includingmovementinamediumandreflection,canbeobservedinsprings.

Figure61-2Generatingastandingwave.CourtesyPASCO.

211

Project62

Rollinguphill.

TheIdea

Mostpeoplewillnotseetheresultsofthislittledemonstrationcoming,especiallyifit’sdoneasanimmediatefollow-upto

thepreviousproject.YoucanmakeacanactuallyrolluphillforashortdistancewithoutviolatinganyofNewton’slaws.

WhatYouNeed

coffeecan

weight—anoldbatteryshouldworkwell

strongglue—suchasGorillaglueorepoxy

incline

Method

1. Gluetheweighttotheinsideofthecoffeecan.

2. Concealtheinteriorwiththeplasticcoverofthecoffeecan.

3. Placethecanontheinclinewiththemassontheuphillsideofthecan’scenterline.SeeFigure62-1.

4. Asksomeoneobservingthiswhattheythinkwillhappen.Youcanaddtotheeffectbycreatingtheillusionthatyou

areinvestigatingoneofthesituationsofthepreviousdiscoverybyusingtwocoffeecanswithweights.

212

Figure62-1Gravitycreatesatorqueonthecancausingittorolluphill.

ExpectedResults

Oncereleased,thecanrollsuphillafewinches.

WhyItWorks

Gravity pulls on theweight, which exerts a torque on the can. If theweight is positioned on the uphill side of the can’s

centerline,thecanwillrolluphill(untiltheweightisbroughtdirectlyunderthecan’scenterofgravity).

OtherThingstoTry

Anothersimilarideaistoattacharubberbandwithaweightinthemiddletotheinsideofthecan.Asthecanrolls,therubber

bandiswoundup.Whenthecanrolls,itreachesaturningpoint,andthenreturnsbackinthedirectionfromwhichitcameas

therubberbandwiththeweightunwinds.

ThePoint

213

Iftheforceexertedbygravityonanobject’scenter-of-massproducesatorqueontheobject,theobjectcanbrieflyrolluphill.

214

Project63

Gettingaroundtheloop.Fromhowfarabovethegrounddoestherollercoasterneedto

start?

TheIdea

Energyisconserved.Anobjecthaspotentialenergybecauseit isacertaindistanceabovetheground.Asitrollsdownan

incline,someofitsenergychangesintokineticenergy

WhatYouNeed

aluminumtrackusedtosecureshelvinginbookcases.Thisisthetypehungverticallyonthesidesofthebookshelf

andholdsclipsthatsupporttheshelves.Thistrackshouldbeflexibleenoughsoyoucanbendittoformacircular

shape.(Youdon’twanttheheavy-dutyshelvingtracksyouwouldusetosetupabookshelftoholdallyourphysics

textbooks.)

1marbleorsteelballthatsmoothlyrollsinthetrack

circularobjecttouseaguide,suchasasmallbucketoraonegallonpaintcan

Figure63-1Wheremusttheballbepositionedtomakeitaroundtheloopwithoutfalling?

frametomounttheframeon

–incline(2feetlong×3incheswide×¾inchthickwilldofine)–bottom3feet×3inches×¾inches–verticalbrace1foot×3inches×¾inch–smallright-anglebrackettosupporttheverticalbrace

youmaywanttoaddsomekindofnettocatchthemarbleattheend,soyoudon’thavetochaseiteverytime

smallflat-headwoodscrews—thesmallerthebetter,butjustlargerthanthescrewholesinthetrack

ameterstick

Thisapparatusisalsocommerciallyavailable,asshowninFigure63-2.

Method

Buildingthetrack

215

1.Assembletheframebyattachingthepiecesofwood,asshown.

2.Formacircularloopbycarefullybendingthetrackaroundtheform.Note,thechannelshouldbetowardtheinsideof

thecirclewhenyoudothis.

3.Predrillholesforthewoodscrewsinthewoodusingadrillbitasizeortwosmallerthanyourscrews.

4.Securethelooptotheframeusingthewoodscrews.Itisimportantthatthe(flat)headsofthewoodsscrewsdonot

interferewiththemotionoftheball.Ifyoufindyourwoodscrewprotrudesintothepathofthemarble,youcanwork

around this by enlarging the holes or by countersinking the holes in the track, so the screw head is flushwith the

bottomofthetrack.

Figure63-2CourtesyPASCO.

5.AlignthetrackasshowninFigure63-1.Theloopshouldbeassymmetricalaspossiblewiththeoverallpathmakinga

verticalloop.Also,makeenoughseparationbetweenthepartofthetrackgoingintoandoutoftheloop,sothereis

enoughclearancebetweenthemarbleandthetrack.

6.Youcan(optionally)attachsomekindofcatcher(anetorcup)toavoidchasingmarbles.

Testingit

1.Takeaguessastowherethemarblemustbeplacedtonegotiatetheloop.Herearesomechoices:a)equaltothe

radius,b)equaltothediameter,c)greaterthanthediameter,ord)twicethediameter.(Takeintoaccounttherewillbe

somefriction.)

2.Pickyourstartingpointandobservewhathappens.Findtheminimumpointtoconsistentlynegotiateoneloop.What

happenstothemarbleifyoureleaseitatapointthatishigherorlowerthanthisminimumpoint?SeeFigure63-1.

Figure63-3CourtesyPASCO.

ExpectedResults

Withalow-frictionslidingobjectcar,suchasacartwithwheelsorarollercoastercar,theheightmustbeatleast2.5times

theradiusoftheloop.Actualloopsrequireslightlygreaterheighttoovercomefriction.

Forrollingobjects,suchasasteelballormarble,someofthepotentialenergyistiedupinrolling,sotheheightmustbeat

least2.7timestheradiusoftheloop(again,withoutaccountingforfrictionallosses).

216

WhyItWorks

Thepotentialenergyyoustartwith(byraisingittocertainheightonthetrack)ischangedintokineticenergy.Thehigheryour

releasepoint, thefaster itgoes. If theobject isrollingratherthansliding,someofthepotentialenergy isusedtogetthe

objectrolling.Ifthereisfrictionalongtheway,someadditionalpotentialenergyisconsumed.

Tonegotiatetheloop,thecentripetalforce(providedbythetracktomaintainacircularpath)mustjustequaltheforceof

gravity.With lessvelocity, itwill fallbeforecompletingthe loop.Withextravelocity, itwillgetthroughwithsomeenergyto

spare.

OtherThingstoTry

Nowthatyouhaveoneloopdown,youcantryasimilartrackwithmorethanoneloop.Youstillonlyneedoneramptogive

themarbleaninitialvelocity.

ThePoint

Totalmechanicalenergyisconserved.Potentialenergyisconvertedtokineticenergyandviceversa.

217

Section6

SoundandWaves

Project64

Whatdoessoundlooklike?Oscilloscopewaveforms.

TheIdea

Whatdoesyourvoiceprintlooklike?Youcannotseesound.Butyoucanchangethesoundwavesintoelectricalsignalsthat

canbedisplayedonascreen.Justasyoufoundwaystovisualizemotionandtorepresentmotionusingvariousgraphs,in

thissectionyoudeveloptechniquestovisuallyrepresentwaves.Thiscanenableyoutostudybasicwavepropertiesandto

observehowwavescombinetoformnewpatterns.

Youcangoaboutthisintwoways.Onewayistouseanoscilloscope,whichisaninstrumentthattakesanelectricalsignal

anddisplaysitingraphicalform.Recently,amuchlowercostalternativehasbecomeavailablethatmakesitpossibletoturn

acomputerintoanoscilloscope.

Thisprojectfocusesonhoweithertypeofoscilloscopecanbeusedtostudythewavepropertiesofsound.

WhatYouNeed

oscilloscopes,whichrangeincostfromjustunder$600tothousandsofdollars

soundcardoscilloscope.Youcanturnyourcomputerintoaoscilloscopeinseveralways:

– PC sound card distributed for private and noncommercial use in educational institutions at

www.zeinitz.de/Christian/Scope_en.html. (Oscilloscope images shown in this and other sections are based on this

soundcardoscilloscopeandappearcourtesyofC.Zeinitz.)

–Zelscopeisavailableforasmallchargeatwww.zelscope.com(thisusedtobecalledWinscope).

tuningfork

adapters

–Toconnectmicrophonetocomputer.Microphonesareeitherhigh-or low-impedanceconnectionsandthecomputer

inputistypicallyamini.

–Microphoneoutputtooscilloscopeinput(typicallyBNCconnector).

–Dependingspecificallyonwhatconnectionsyouneedtomake,youcanmostlikelyfindconnectorsatRadioShackor

buildtheconnectoryouneed.

–Caution:Soundcardoscilloscopescanhandleonlylow-voltageinputs,suchasfrommicrophones.Attemptingtousea

soundcardoscilloscopeforlargerelectricalsignalmaydamageyoursoundcard.Areferenceforhowtoassemblea

high-impedancecircuitthatcanenableusingasoundcardoscilloscopeforhighervoltagesisgiveninProject115.

wavegenerator

–stand-alonedevicedesignedforthispurpose

–keyboardwithappropriateconnectors

–waveformgeneratoravailablewithsomecomputeroscilloscopes

Method

218

Settinguptheoscilloscope

1. Connectthemicrophonetotheoscilloscopeinput.

2. Collectatestsignal,suchasyourvoiceoramusicalsound.

3. Adjusttheverticalscale,sotheentirewaveisdisplayed.

4. Adjustthehorizontal(time)scale,sothewaveisdisplayed.

5. Ifnecessary,adjustthetriggertoenablethewavetobeproperlydisplayed.(Chosecontinuousratherthansingle-

eventsettingsforthetrigger.)

Displayingwaves

1. Generateapitchaudiblywithatuningfork,akeyboardsynthesizer,orbyawaveformgenerator.(Dependingonyour

setup,youcanusethewaveformgeneratortoproduceanaudiblesignalthroughaloudspeakerorsenditdirectly

intotheinputoftheoscilloscope.)

2. Increasethepitch(frequency)andcomparetothepreviousshape.

3. Decreasethepitchandcomparetothepreviousmeasurements.

4. Increasethevolume(amplitude)ofthesoundandobservehowthewavechanges.

5. Tryyourvoiceusingthemicrophone.Howdoesthatcomparetoapuretone,suchasproducedbythetuningfork?

6. Observedifferentwaveformshapes,suchassinusoidal,triangular,squarewave,andsawtooth.Howdotheysound?

Whatmusicalinstrumentsdoeachofthepreviouswaveformsmostcloselyresemble?

7. Playvariousmusicalinstrumentsandidentifyfundamentalwaveformsthatappeartobepresentintheinstruments’

waveforms.

8. Just for fun:Observe varioussamplesofmusic.Can youdistinguish variousmusical styles justby lookingat the

waveform?

9. Canyourecognizethe“voicesignature”ofdifferentpeopleascrimelabsdoallthetimeonTV?

Addingwaves

1. Generateatoneorfrequency.Let’ssaywestartwith440hertz(Hz),aconcertA.DisplaythisonChannel1.

2. Generateasecondtoneorfrequency.Let’ssayweuse100Hz.DisplaythisonChannel2.

3. Manyoscilloscopesletyoudisplaytwosignalsononedisplay.Ifyouroscilloscopehasthecapabilitytodisplaytwo

inputsononedisplay,showthecombinedsignalsfrom1and2.Howdoesthecombinedsignalcomparetothetwo

individualsignals?

4. Youcanalsoaccomplish thisbygenerating twoaudible tonesat thesametime,suchasplaying twonotesona

keyboardsynthesizeratthesametime.Soundingtwotuningforksatthesametimewillalsowork.

ExpectedResults

Increasedpitchshowsupontheoscilloscopeasincreasedfrequency.

Increasedvolumeisdisplayedasincreasedamplitude.

A tuning forkorawavegeneratorproducesapuresinewave.Figure64-1shows the relativelypure sinewavepattern

producedbytheflutesettingofanelectronicsynthesizerplayinga440Hztone.

Sawtoothandtriangularwavessoundmore“reedy,”likeaclarinetorsaxophone.

Othersoundsarecomplexmixturesofsimplerforms.Forinstance,asynthesizedrockorganconsistsofawiderrangeof

overtones combined with the fundamental tone. Figure 64-2 shows several higher frequencies combined with a 440 Hz

fundamental.

219

Figure64-1Synthesizerflutesetting.

220

Figure64-2Synthesizerrockorgansetting.

221

Figure64-3100Hztone.

Addingtwowaveformsresultsinacombinedsound.Figure64-3showsa100HztoneandFigure64-4showsa400Hz

tone.

Figure64-5showsbothofthesetonescombined.Theoverallpatternshowshowbothofthesetonesaddtoproducea

combinedwavepattern.

Musical sounds are complex mixes of many individual frequencies with a large variety of overtones. Figure 64-6 is a

samplefromTheBeatlesandFigure64-7isanAllisonKrausefiddlesolo.

Anoscilloscopecanalsoshowthemixoffrequenciesinaparticularsound.Forinstance,asynthesizerviolinsoundwhen

playinga440Hztonealsohassomeovertonesat880Hzand1360Hz,asshowninFigure64-8.

222

Figure64-4400Hztone.

223

Figure64-5100Hzcombinedwith400Hztones.

224

Figure64-6“EleanorRigby”byTheBeatles.

Themixofovertonescontributestoestablishingthemusicalidentitiesofvariousinstruments.Forinstance,arecorderhas

a very pure tone with very few overtones. Other sounds, such as a rock organ or a distorted bass, have amuchmore

complexmixofovertones.

WhyItWorks

Anoscilloscopeprocessesanelectricalsignalanddisplaysit invariousways.Theoriginoftheelectricalsignalmaybea

microphonethatconvertsasoundpatternintoanelectricalpattern,whichtheoscilloscopecanworkwith.Themostbasic

formofdisplayisasinglesignalversustime.Thescalesareadjustabletopermitawiderangeofsignalstobedisplayed.

Oscilloscopesalsodisplaytwosignalsbothindividuallyonthesamescreenoradded.Aplotofonesignalagainsttheother

andadistributionoffrequenciesarealsocommonoptions.

225

Figure64-7Thehigh-lonesomesoundofabluegrassfiddle.

226

Figure64-8Frequencydistributionofa440Hzviolintoneshowingovertones.

OtherThingstoTry

Hereisalow-techwayofpicturingsound:Coverasoupcan(clean,empty,andwiththetopremoved)withLatexorother

rubberymaterial.Put iton tight, likeadrum.Attach itwithawire tie, hoseclamp,orgoodstring.Glueasmall (roughly1

centimeteronaside)pieceofmirrortothetopoftheLatex.Touseit,holdthecaninonehandandshinealaseronthe

mirror,so thebeamprojectsonto theceiling (orawall). If youdon’thavea laser,directsunworksaswell.With the light

reflectingoffthemirror,createsoundsthatwillcausetheLatextovibrate.Becauseoftheopticalgeometry,themovement

ofthereflectedlaserislarger(amplified)thanthesmallermovementofthemirror.Becausethe“drum”willbevibratingintwo

dimensions,itisnothardtogeneratetheLissajouspatternswherethereflectedlightretracesacurvedpath.

ThePoint

Soundisawavethat,ifconvertedintoanelectricalsignal,canbedisplayedinagraphicalform.

227

Project65

Rippletank.

TheIdea

Waterwavesareprobably themost tangible typeofwave. For this reason,waterwavescanbe useful in studyingwave

propertiesingeneral.Arippletankprovidesasimple,convenientwaytoproduceandstudywavesandthevarioustypesof

obstaclestheycanencounter.

WhatYouNeed

shallowtrayortankwithatransparentbottomorcommerciallyavailablerippletank

water

brightlightthatcanbeheldormountedabovethetank

oneorseveralplainsheetsofwhiteposterboardtoserveasascreenonwhichtoviewtheimagesproducedbythe

rippletank

variouspropsincludingastraightwall,acurvedwall,athickglassplateaboutone-halfthethicknessofthewaterin

thetank,acup,apencil,andamanualormechanicalsourceofripples

optional:awaytoprojecttheshadowsgenerated,suchasanoverheadprojectoravideomonitor

Method

Basicwavegeneration

1. Setupthetankwiththelightoverhead.Theshadowpatternshouldbevisibleonthefloor.

2. Adjusttheheightofthelightabovethetankandthescreenbelowthetanktogivethebestfocusoftheshadows

fromtheripplesonthefloor.

3. Usingthetipofaruler,tapthesurfaceofthewatertoproduceripples.Ifyouhaveavibratingripplegenerator,using

thatmightgivemoreconsistentresultsandyouwon’tgettiredasquicklyfrommakingripples.

4. Youshouldseetheripplesspreadoutinacircularpattern.Thetankshouldbelargeenough,sothisoutwardmoving

circularpattern isnotobscuredbythereflectionof theripplesfromthesideof thetank.Sometimes,aborderof

foamcushioningisusedtominimizesidereflections.

5. Estimatethewavelength(averagedistancebetweenripples)andfrequency(numberofripplespersecond).Estimate

the velocity of the ripples. Compare this with the velocity predicted by the wave equation (which applies to all

waves):velocity=wavelength×frequency(incyclespersecond,whichisthesameashertz). Ifyoumeasurethewavelengthincentimeters,thevelocitywillbeincentimeterspersecond.

Reflection

1. Insertastraightbarrier—awall—inthetank.

2. Generateripplesmovingtowardthebarrieratvariousangles.

3. Observetheanglethereflectedwavesmakecomparedwiththeincomingwaves.

228

Figure65-1Rippletankshowingshadowsofwavepatternsonwhiteboard.

Concaveandconvexcurvedreflector

1. Inserttheconcavereflector.Thisiswherethesidescurvetowardthesourceoftheripples.Observehowthewaves

arereflected.Dothewavesconvergeordiverge?

2. Generateripplesthatoriginateatthatfocalpoint.Howdotheripplesmove?

3. Insert(orreshape)thereflector,soitisconvex.Thisiswherethesidescurveawayfromthesourceoftheripples.

Dothewavesconvergeordiverge?

Refraction

1. Placeathickplateinthetank.

2. Whathappens to thespeedof thewavesas thewavescrossover theplate?Whathappens to thewavelength?

Doesthismakesensegiventhatthefrequencydoesn’tchange?

3. Directwavestotheplateatanangle.Whathappenswhenthewavescrossfromthedeepwatertotheshallower

water?

Diffraction

1. Generateripplesandobservewhathappenswhentheyencounterapencilheldverticallyintheirpath.

2. Whathappenswhenalargerbarrier,suchasaglassorbeaker,isheldinthepathoftheripples?

Interference

1. Generate ripples from twodifferent locations.The ripplesshouldbesynchronized insuchaway thateach ripple

makergoesupatthesametimeanddownatthesametime.(Thismeansthesourcesofthewavesareinphase.)

2. Observewhathappenstothepatternasthewavesfromthetwosourcesoverlapandinteractwitheachother.

ExpectedResults

Straightbarrier:theincomingangleequalstheoutgoingangle.

Concavebarrier:thereflectedwavesconvergeatafocalpoint.

229

Concavebarrier:ripplesgeneratedatthefocusregroupandemergeasasinglewave.

Convexbarrier:wavesdivergefromanylocation.

Plate:thewavesslowastheycrossovertheplate;thewavelengthincreases.

Plate:thewavescomingtowardtheplateatananglearebenttoaless-severeangle.

Figure65-2Ripplepatternscrossovertheconvexshapedbarrier,resultingintheconvergenceofthewavepattern.Courtesy

PASCO.

Figure65-3Thisrippletank(withverticaldisplay)showsthediffractionpatternproducedbytwoseparatesourcesofwave

generation.CourtesyPASCO.

Diffraction:thewavefrontsregrouparoundasmallbarrier,butnotalargerone.

Interference:tworipplelocationsresultinafixedpatternofhighandlowwaves.

WhyItWorks

Waterwavesexhibitbasicwaveproperties,including:

Reflectionfromstraightsurface:Angleofincidenceequalsangleofreflection(withallanglesdefinedwithrespectto

theperpendicularornormallinethatcanbedrawntothereflectingsurface).

230

Reflectionfromaconcavesurface:Wavesarereflectedfromacurvedsurfacewiththelawofreflectionapplyingto

thetangentlineofthecurveatthatpoint.Forapproximatelyparabolicreflectorsthatincludesemicircularreflectors,

this results inwavespassing througha focal point. If thewavesaregeneratedat that focal point, they become

focusedandpropagateinasingledirection.

Reflection from a convex surface: Waves diverge and propagate over a wider range of angles than when they

started.Thereisnofocalpointwhenwavesreflectfromaconvexsurface.

Refraction:Wavesbend toward theperpendicular line (called thenormal line)when theyentera regionwhere the

lightwavesmovemoreslowly.

Diffraction:Waves bend around a barrier in their path if the diameter of that barrier is small comparedwith the

wavelength.

Interference:Crestsandtroughsofwavescombinetoformanoverallpatternbasedonconstructiveanddestructive

interference.

OtherThingstoTry

Alargestationarybodyofwatercanserveasalargerippletank.Inthiscase,travelingwavescanbeobservedwithoutthe

complicationofreflectionsfromthesideoftherippletank.PicturedinFigure65-4isaninterferencepatternformedbytwo

rocksthrownintoalake.

ThePoint

Wavesexhibitcertaincharacteristicbehavior, includingreflection, refraction,diffraction,and interference.Theseproperties

arecommontoalltypesofwaves.

Figure65-4Tworocksformaninterferencepatternastheripplestheyproducespreadacrossthesurfaceofalake.

231

Project66

Simpleharmonicmotion.Theswingingpendulum.

TheIdea

Apendulumundergoesatypeofmotionthatispredictable.Theconsistencyofpendulummotionhasallowedittobeusedto

drivethetimingmechanismofclocks.Inthisexperiment,youinvestigatewhatcausesapendulumtoswingfasterorslower.

AtleastforapendulumonthesurfaceoftheEarth,onlyonevariabledeterminesthetimeittakesforapendulumtoswing

backandforthonetime.

WhatYouNeed

severalmassesthatcanbeattachedtoastring(suchas20g,50g,100g,200g)

severalstringsofvaryinglengthsfrom0.1to1.0m(strongenoughtosupportthemasses)

supportforeachpendulum

stopwatch

meterstick

Method

1. Setupabasicpendulumwithameasuredlengthandmassfreetoswing.

2. Pullthependulumbacktothesidethroughasmall(lessthan15degrees)angleandgetthestopwatchready.

3. Releasethependulumandstartthestopwatchasthependulumisreleased.

4. Counttencyclesbackandforth.Cyclenumberoneiswhenthependulumreturnstoitsoriginalposition.Becareful

nottocount“one”whenthependulumisreleased.

5. Thelengthofthependulumisthedistancefromthepointwherethestringissupportedtothecenterofthemass.

6. Recordthetime(inseconds)forthependulumtocompletetencompletecycles.

7. Dividethetimefortencyclesbytentogetthetimeforonecycleortheperiodofthependulumfortheconditions

youaretesting.

8. Youcanproceed inseveralwaysat thispoint,withmanyopportunitiestodevelopyourownplan.Hereareafew

suggestions:

– What variable matters: Mass? Length? Angle? Test the selected variable while holding the others constant. For

instance,testlight,medium,andheavymass,andthendeterminewhethertheperiodofthependulumisdependenton

mass.Thiscanbedonebymeasuringtheperiodofapendulumconstructedwitheachofthethreemasses.Itcanalso

bedonequalitativelybysettingupthreependulaandobservinghowfasttheyswingcomparedtoeachother.

–Onceyoudeterminewhichvariable(s)affectshowfastthependulumswings,youcansetupanexperimenttomeasure

howtheperiodchangesoverarangeofthevariablesyouselected.Theothervariablesshouldbekeptconstant.

232

Figure66-1Simpleswingingpendulum.

ExpectedResults

Theonlyvariablethataffectstheperiodofapendulumislength.Themassdoesnotmatteratall.Foranglessmallerthan

15degrees,angleisinsignificant.Insignificantmeanslessthan1percent.

Thelongerthestring,thelongertheperiod(periodisthetimetogobackandforthonetime).

Thedependenceofperiodonlengthisnotlinear.

233

Figure66-2Periodversuslengthforapendulum.

AgraphofperiodversuslengthisshowninFigure66-2.Themodelforthegraphshowstheperiod isdependentonthe

squarerootofthelength.

WhyItWorks

Theperiodofapendulumisthetimeittakesforthependulumtomovefromonepositionandreturntothesameposition.

Theperiodofapendulum(inseconds)isgivenby:

whereListhelengthofthestring(inmeters)andgisthegravitationalacceleration(9.8m/s2).

Thisshowsthedependenceonthesquarerootofthestringlength.Becausethereisnomassintheequation,theperiod

does not depend onmass. The period also depends on the gravitational acceleration of the Earth, which under normal

circumstancesisnotavariable.

OtherThingstoTry

Trythiswithapendulum,consistingofabowlingballattachedtoarope.Makesurethepointofattachmentandtheropecan

securelyhandletheweightoftheswingingpendulum.

Trythiswithaplaygroundswing.Isthenaturalfrequencyofoscillationwhatyoupredictbasedonthepreviousequation?

Whathappensifyoupushwitharhythmconsistentwiththatnaturalfrequency?Whathappensifyoupushwitharhythmvery

differentfromthenaturalfrequency?

ThePoint

Theperiodofapendulumdependsononlyonevariable,whichisitslength.

234

Project67

Simpleharmonicmotion.Thespringpendulum.

TheIdea

Amasshangingfromaspringisanotherexampleofasystemthatmovesinarepeatableandconsistentway.Thisiscalled

simpleharmonicmotion.Thisexperimentisaboutfindingwhatcausesaspringpendulumtovibratefasterorslower.

WhatYouNeed

severalmassesthatcanbeattachedtoastring(suchas20g,50g,100g,200g)

several springs of varying stiffness—it should be possible to partially stretch the spring by hanging each of the

masses to thebottomof thespring. If themassescan’tstretch thespringor if thespring is fullyextendedwhile

supportingthemass,chooseeitherothermassesorothersprings

supportforeachpendulum

stopwatch

meterstick

springbalance(fortheextension)

Method

1. Setupaspringpendulumconsistingofaspringwithoneendsupportingamassandtheotherattachedtoasupport

abovethespring.

2. Allowtheweightofthemasstostretchthespringandcometorest.

3. Pullthependulumstraightdownthroughasmalldisplacement.(Increasingtheelongationofthespringbyabout10

percentisagoodstartingpoint.)

4. Releasethependulumandstartthestopwatchasthependulumisreleased.Trytoreleasethespring,soitgoesup

and down in a vertical direction. Bear in mind that, after a few cycles, a spring may have a tendency to start

swinging,whichcomplicatesthetypeofmotionweareinvestigatinghere.

5. Counttencyclesupanddown.Cyclenumberoneiswhenthependulumreturnstoitsoriginalposition.Becarefulnot

tocount“one”whenthependulumisreleased.

6. Recordthetime(inseconds)forthependulumtocompletetencompletecycles.

7. Divide the time for ten cycles by ten to get the time for one cycle. This is the period of the pendulum for the

conditionsyouaretesting.

8. Aswiththepreviousstudy,youcanapproachthisinvestigationinseveralways.Youareencouragedtodevelopyour

ownapproachtothis.Hereareafewsuggestions:

–Whatvariablematters:Mass?Springstiffness?Amountofdisplacement?Testtheselectedvariable,whileholdingthe

others constant. For instance, you can test squooshy, medium, and stiff springs, all using the same mass and

displacement.(Wedefine“squooshy”inquantitativetermsinaminute.)Similarly,youcantestlight,medium,andheavy

masstodeterminewhethertheperiodofthependulumisdependentonmass.

235

Figure67-1Springpendulum.

–Onceyoudeterminewhichvariable(s)affectshowfastthependulumswings,youcansetupanexperimenttomeasure

howtheperiodchangesoverarangeofthevariableyouselected.Theothervariablesshouldbekeptconstant.

ExpectedResults

Thebehaviorofthespringpendulumisquitedifferentthantheswinging(simple)pendulumstudiedinthepreviousproject.

Twovariablesareimportantforaspringpendulum:massandspringstiffness.

Theheavierthemass,thelongertheperiod.Also,thestifferthespring,theshortertheperiod.The“springiness”ofaspring

iscalledthespringconstant,whichgivesanumericmeasureofhowstiffaspringis.

Within a fairly broad range, it should not matter whether you pull the spring through a small displacement or a larger

displacement.

Thedependenceofperiodonmassandspringconstantisnotlinear.

WhyItWorks

Theequationfortheperiodofaspringpendulum(inseconds)isgivenby:

236

wheremisthemass(inkilograms)andkisthespringconstant(inN/m).Noticetheperiodvariesasthesquarerootofthe

massandtheinversesquarerootofthespringconstant.

OtherThingstoTry

Predictandmeasuretheperiodofthespringpendulum.Youcandothisbyfirstfindingthespringconstantusingthemethod

ofProject30.Youfindthespringconstant,k,bymeasuringthedisplacement,x,ofaspring(inm)resultingfromagivenforce,

F(inN),accordingtotheequation:

k=–F/x

Thenegativesignreflectsthefactthatforceanddisplacementarealwaysintheoppositedirectionresultinginapositive

valuefork.

Onceyouhavedeterminedthespringconstant,predicttheperiodofthespringpendulumusing:

(Theperiodwillbegiveninsecondsiftheforceisenteredinnewtonsandthedisplacementinmeterstogetk.Themass

must be in kg. Remember 1000g= 1kg.)Once you’ve called your shots, set your pendulum inmotion and compare your

predictionwithyourmeasuredresult.

ThePoint

The period of a spring pendulum increasesas the square root of themass.Theperiod of a spring pendulum increases

inverselywiththesquarerootofthespringconstant.

237

Project68

Generatingsinewaves.

TheIdea

Thesimplicityofthespringpendulumprovidesanexcellentopportunitytoobserveitsmotionindetail.Themovement, like

othervibrationsinnature,followsasinewave.Wecanalsoidentifyparticularpointsinthespring’smovement,suchaswhere

thevelocityisatamaximumandaminimumduringitscycle.Wecanalsomonitorhowtheforcevariesandhowitrelatesto

the acceleration. These relationships form the basis for amore complete understanding of how the various aspects of

motionareinterrelated.

WhatYouNeed

springpendulum—setupasinpreviousexperiments

Method

1.Setthependuluminmotionandfirstobservewhenthefollowingoccursinthecycle:

–Zerovelocity

–Maximumvelocity

–Zeroforce

–Maximumforce

–Zeroacceleration

–Maximumacceleration

2. Place amotion sensor to view themotion of the spring pendulum from underneath. If themass presents a small

target,youcantapeanindexcardtothebottomofthemasstomakeiteasierforthemotionsensortofind.(Toavoid

airresistance,keepitsmall.)

3.AdjustthesettingsintheDataStudioprogramtogivethemaximumnumberofreadingspersecond.

4.Openfilestoreadsimultaneously:distance,velocity,andacceleration.

5.Displacethespringandbereadytoreleaseit.

6.PressStartontheDataStudioscreentobeginloggingdata.

7.Releasethespring.

8.Recordafewcycles.

9.Adjust thescales, if necessary, tobestdisplay thecharts.Use thesmoothing tools, if needed, togiveasmoother

curveiftheaccelerationdataappearsslightlychoppy.

ExpectedResults

Theequilibriumpositionisthepointwherethestationarymasshangswithoutmoving.Attheequilibriumposition,thevelocity

ismaximum,buttheforce(and,therefore,theacceleration)iszero.

Atthemaximumdisplacementposition(thepointfromwherethespringwasreleased),thevelocityiszeroandtheforce

(and, therefore, theacceleration) ismaximum.Graphsgeneratedbyamotionsensormeasuringapendulumareshown in

Figure68-1.

238

Figure68-1DataStudiographsofmotionsensordatashowingdistance,velocity,andaccelerationversustime(setupbyT.

DragoiuandJ.Silver).

Thedistanceversustimegraphisasinewave.

Thevelocityversustimegraphisacosinewave.Thevelocityiszerowhenthedistanceisatamaximum.Thetwowaves

haveasimilarshape,butthevelocitycurveisdelayedbyone-quarterofaperiodcomparedtothedistancecurve.

Theaccelerationcurveisalsoasinewave.Itisataminimumwhenthedistanceismaximum.Theaccelerationcurveis

zerowhenthedistancecurveiszero.Thedistanceandaccelerationcurveshaveasimilarshape,excepttheacceleration

curveisdelayedbyone-halfofawavelength.

WhyItWorks

Apendulumworksbecausethefurtherthemassmovesfromequilibrium,thegreatertheforcethatreturnsittoequilibrium.

Thisisthebasisofanyuniformlyvibratingobject(knownasasimpleharmonicoscillator).Theresponseofarestoringforce,

suchasexertedbyaspring,istoproducemotionthatfollowsasinewave.Theaccelerationmovesintheoppositedirection

asthedistancebecausetheforceexertedbyaspringisoppositeitsdisplacementfromequilibrium.Thisalsocausesthe

velocityandaccelerationcurvestobeoutofphasewithrespecttothedistance.

OtherThingstoTry

Avariationonthisistoattachaforcegaugetothespringtotracktheforcealongwiththemotionofthependulum.

Physicsalert:Thoseofyoufamiliarwithcalculuswillrecognizethatvelocityisthefirstderivativeofdistance.Acceleration

isthefirstderivativeofvelocityandthesecondderivativeofthedistancewithrespecttotime.Ifthedistancefollowsasine

curve,thevelocity(thefirstderivative)isacosinecurveandtheaccelerationisasinecurve.

ThePoint

Aspring is a simple harmonic oscillator whose distance follows a sine wave pattern. Velocity and acceleration follow a

similarshape,butaredelayedwithrespecttothedistancecurve.Thevelocityisatamaximumatthepointofthegreatest

displacement.Accelerationisatamaximumatthepointofgreatestextension.

239

240

Project69

Naturalfrequency.

TheIdea

Whenyoupushsomeoneonaswing,timingisimportant.Ifyoupushjustastheswinghascometoitshighestpointandis

readytobeginitsreturn,youwillkeeptheswinggoingandincreaseitsamplitude.However,ifyoupushrandomly,yourefforts

willbefar lesseffectiveand,attimes,youwill tendtoslowthemotionoftheswing.Thereasonforthis isaswinghasa

naturalfrequency.Ifyourpushingisatthenaturalfrequencyoftheswing,theswingwillresonate.Thisexperimentexplores

theideaofresonance.

WhatYouNeed

2ringstands

1⅜inchdiameterwoodendowel,12incheslong2clamps(toholdthedowel)

stringofvariouslengths,fromabout3inchesto10inches

setof several smallmasses thatcanbeattached to thestring (largestainlesssteel nutsworkwell hereorany

attachablemassesintheoverallrangefrom10–50g)

Method

1.Tieloopsatoneendofeachofthestringsandtietheotherendtoamass.Atleasttwoofthestringsshouldbethe

same length. The other should be random—some larger and some smaller than thematched pair. Avoid, however,

havingalltheotherstringshalfordoublethesizeofthematchedpair.

2.Slidethe loopsontothedowelandspreadthestringsoutevenlyacrossthe lengthofthedowel.Thetwomatched

stringsshouldnotbenexttoeachother.

3.Attachthedoweltothetwouprightpostsoftheringstandsusingtheclamps.Leaveenoughspace,soallthemasses

arefreetoswingwithouthittingthetable,whichtheringstandsareplacedon.Thedowelshouldbeslightlyflexible,but

constrainedbytheringstands,soitwillnotswayorswivelwhenthemassesareswinging.SeeFigure69-1.

4.Steadyallthemasseshangingonthestrings.

5.Takeonlyoneofthemassesonthematchedstringsanddisplaceit,soitisswingingperpendiculartothedirectionof

thedowel.

ExpectedResults

Whatwewanttoseehereisforthestationarystring,whichisthesamelengthastheonethatwassetinmotion,toalso

startmovingbackandforth.Theothermassesmightjostlearoundabit,buttheyshouldnotbesetintoasignificantswinging

motion.

WhyItWorks

Theresonantfrequencyofapendulumisdeterminedexclusivelybythelengthofthestringthatsupportsit.Thestationary

pendulumisstimulatedbytheswingingpendulumthathasthesamelengthand,therefore,thesamenaturalfrequency.

241

Figure69-1Resonantfrequencydependsonlyonstringlength.

OtherThingstoTry

Otherquestionsthatcanbeaddressedare:

1.Wouldapendulumwiththesamestringlength,butdifferentmass,havethesameresonantfrequencyastheswinging

pendulum?

2.Whatifwethrowinafewharmonics?Whatistheresponseofapendulumthatisone-halfthelengthoftheswinging

pendulum?Whatistheresponseofapendulumthatisdoublethelengthoftheswingingpendulum?

ThePoint

Asimpleharmonicoscillator, suchasaswinging (simple)pendulum,hasanatural frequency. If stimulatedat that natural

frequency,theamplitudeofthatpendulumwillbegreatest.

242

Project70

Bunsenburnerpipeorgan.Resonantfrequency.

TheIdea

If youblowacross the topofasodabottle, youproduceasound.Themoresodayoudrink, thedeeper thepitchof the

sound.This isbecausetheresonantfrequencyofthebottle increasesastheheightoftheairabovethe liquid increases.

Thisprojectdoesthesamething,exceptonamuchbiggerscale.Youuse longertubesthatproducedeepersounds.You

may just want to give the person who is responsible for the building you are in (such as the building principal) advance

warningthatthesoundtheywillbehearingisnotanearthquake,notawaterbuffaloinlabor,andnotthepropulsionsystem

foraspacealienspacecraft.

WhatYouNeed

largeBunsenburner

cylindricaltubesroughly0.8–2metersinlength—goodcandidatesforthisarecardboardtubesusedforcarpetrolls

orhollowmetalsectionsofolddrivewaybasketballbackboardsupports

fireextinguisherand/orbucketofwater(youshouldnotneedthis,butjustincase)

Method

1. PlacetheBunsenburneronthefloor.

2. Routeahoselongenoughnottogettangledandconnectittoanaturalgasoutlet(which,atthispoint,isnotturned

on).

3. Positionacylindricaltubeonthefloor,soitcaneasilybeplacedovertheburner.

4. Lighttheburnerandadjustit,sotheflowismaximum,withthegreatestflame.

5. Make sure nothing flammable is near the burner, including possible objects on the ceilingand loosepapers that

mightinadvertentlybedrawnintotheflamebyconvections.

6. Liftthecylinderwithbothhandsandpositionitabovetheburner.Holditafewinchesabovethetopoftheburner,

butnotsolowthatitconstrictstheairgoingintotheburner.SeeFigure70-1.

7. Be somewhat careful toavoid charring theedgeof the tube.Donot hold theedgeof the tubedirectly over the

flame.Ifheldcorrectly,thetubewillnotburn.Alsoexercisesimilarcaretoavoidexcessivelyheatingametaltube,

whichcouldpossiblyresultinaburninghazard.

8. ItmaytakeasmuchasaminuteorsountilasufficientstreamofexhaustfromtheBunsenburnerflowsthroughthe

tubetoproduceanacousticresonance.

9. Measure (or, if you prefer, observe) the pitch (or frequency) of the sound produced using the pitch gauge or

oscilloscope.Youcanalsocomparethepitchwithaknownfrequency,suchasproducedbyhittingatuningforkor

soundingamusicalinstrument.

10. Removethecylinderanddon’tforgettoturnofftheburnerwhenyouarefinished.

243

Figure70-1Resonatingtube.

ExpectedResults

Withasufficientflowofheatedair,thetubeshouldresonate.Thetallertubesproduceamuchlowerpitchthantheshorter

tubes.Thediameterofthetubedoesnotaffectthepitch,butitmayaffectthevolumebyimpactinghowmuchaircanflow.

Foragivenlength,thefrequencyofthetubeisgivenby:

The shorter columns produce tones consistent with the sounds of common concert instruments. The longer columns

produceverydeep,resonantpitches.

WhyItWorks

Theflowingair,justlikeawindinstrument,createsaresonantstandingwaveinthetube.Thelongerthetube,thelongerthe

wavelength,buttheshorterthefrequency.

Thefrequencyforanopentubeisgivenbyf=v/2L.Foragiventubelength,thisfrequencyistwiceashighasitwouldbe

foraclosedtube.Refiningthistotakeintoaccounttheslightoffsetofthenodefromtheendsofthetube,theequationis:

f=v/2(L+0.8d)

wheredisthediameterofthetube(inm),Listhelengthofthetube(inm),andvisthespeedofsound(inm/s).

244

OtherThingstoTry

Ifyouhavemorethanonetubewhosediametersaresimilar,youcannestseveraltubestogether,oneinsidetheother,as

showninFigure70-2.Thiscan letyoucontinuouslyvary thepitchof the tube, likea trombone.Youmaywant topractice

beforeauditioningforthespringmusical.

ThePoint

Theresonantfrequencyinanopenpipeislowerforagreaterlength.

Figure70-2Changingthenotelikeatrombone.

245

Project71

Springsandelectromagnets.Resonance.

TheIdea

Ononesideoftheroom,youhaveabarmagnetsuspendedfromaspring.Themagnetissurroundedbyanelectricalcoil,

whichisattachedtoanothercoilontheothersideoftheroom.Anidenticalmagnetisplacedinsidethesecondcoil.Asthe

first coil startsmoving, an electrical current is produced, which also causes the secondmagnet to startmoving. This is

impressive to seeanddemonstratesseveral principlesofphysics, including resonance,magnetic induction,andmagnetic

force.

WhatYouNeed

2barmagnets

2equalsprings

2wirecoilswithan interioropening just largeenoughfor themagnets (thesecanbemadeorareavailablefrom

scientificequipmentsupplycompanies)

2ringstandswithclampstosupportahorizontalconnectingbar;2pendulumclampswouldbeperfect

string

table

connectingwire

optional:4LEDs

Method

Overall,youaregoingtosetuptwoidenticalpartsoftheapparatus,showninFigure71-1,connectedtogetherelectrically.

Todothis,followthesesteps:

1. Suspendeachofthetwospringstothesupports.

2. Attachthetwobarmagnetstothebottomofthespringsusingstringorwire.

3. Positionthebarmagnets,sowhenthespringisdisplaceddownward,themagnetextendsintothecoil,butitdoes

nottouchthetablethecoilsaresittingon.

4. Startwithbothspringshanging.

5. Displaceonespringtosetitoscillating,butleavetheotherspringhangingundisturbed.Observetheresult.

ExpectedResults

Initially,thefirstmagnet,afterbeingsetinmotion,goesupanddownbyitself.Themotionofthefirstmagnetgeneratesan

electricalcurrentthatcausesthesecondmagnet/springcombinationtostarttooscillate.

WhyItWorks

The firstmagnetmoving through thecoil generatesacurrent.This current is transmitted to the secondcoil.Thecurrent

flowinginthesecondcoilexertsaforceonthesecondmagnet,whichsetsitinmotion.Becausebothspringsareamatched

setwithnearly identicalspringconstants,thefrequencyoftheelectricalsignaldrivingthesecondspring isat itsresonant

frequency.Asmalldrivingforceattheresonantfrequencyhasamuchgreaterimpactthanaforceatanyotherfrequency.

246

Figure71-1Themovementofonespringcausestheotheronetoresonate.

OtherThingstoTry

Ifyouwanttopushyourluck,youcanputanLEDintheelectricalcircuit.LEDsconductcurrentinonlyonedirection.Apairof

LEDs,eachorientedintheoppositedirectionandconnectedinparallel,wouldbeneededtopreventblockingthecurrentflow.

Youcanalsoputagalvanometeroracurrentsensorinserieswithoneofthewiresandmeasurethecurrentflowdirectly.

Anothersimplewaytoshowoscillationbetweenmagnetsistosuspendtwomagnetshorizontallyfromsprings.Startwith

thenorthpoleofonemagnetfacingthesouthpoleoftheothermagnet.Then,turneachofthemagnetsfromthatequilibrium

line.Theycanbeturnedthroughanangle inthesameoropposingdirections.Themagnetswillmovetobringthemselves

backtothatequilibriumposition.Buttheywillovershootandkeepgoinguntil theirenergyis losttofriction.Untilthen,they

formasimpleharmonicoscillator.Trythiswithdifferentstartingangles.

ThePoint

Amagnetmovinginacoilofwiregeneratesanelectricalcurrent.

Anelectricalcurrentmovinginawireexertsaforceonamagnet.

Asimpleharmonicoscillator(inthiscase,thespring)resonatesifdrivenatitsresonantfrequency.

247

Project72

Speedofsound.Timinganechooldschool.WhyGalileocouldn’tdothiswithlight.

TheIdea

Thespeedofsound,likeanyothersound,canbefoundbymeasuringthetimeittakestogoacertaindistance.Thissimple

andstraightforwardmeasurementcangiveareasonableballparkestimate,butnothighlyaccurateresults.Wewill,however,

belimitedbythelargedistancesweneedtoworkwithandthesmalltimesweneedtoaccuratelymeasure.Wemeasurethe

speedofsoundusingamoreaccuratemethodinthefollowingprojects.

WhatYouNeed

long tapemeasure (or someotherway toestimatea longdistance, suchascountingcinder blocksofa known

lengthonabuildingorclockingthedistanceofseveralblocksusingtheodometerofacar)

meansofgeneratinga loudsound(suchasanairhorn,garbage-can lid,orbaseballbat,orsomeonewitha loud

voice)

stopwatch

partner(whichmaynotbeneededifyoucansetupanecho)

Method

1. Measureorestimateacourseofknownorestimateddistancewithoutvisualobstruction.Afootballfieldorpossibly

multiple lengthscanwork.Youcanalsouseabuildingornaturalgeographicfeature,suchasacliff toreflectan

echo.Thiseffectivelydoublesthedistancethesoundtravels.

2. Generatethesoundandnotethedifferenceintimebetweenwhenthesoundwasgeneratedandwhenitisheardat

adistantlocation.(Thiscanbeaccomplishedbyobservingwhenthegarbage-canlidwasstruckorobservingata

distancewhentheairhornissounded.)

3. Togetthespeedofsound,dividethedistancebythetime.SeeFigure72-1.

ExpectedResults

Thespeedofsoundisabout343meterspersecondorabout1096feetpersecondat20°C.Itisunlikelythistechniquewillgiveanaccuratevalueforthespeedofsound,butitshouldprovideaballparkestimate.

248

Figure72-1Measuringthevelocityofsounddirectly.

WhyItWorks

Velocityisdistancedividedbytime.Becausethespeedoflightissomuchgreaterthanthespeedofsound,thetimeittakes

lighttotravelthedistancecanbeconsideredessentiallyzeroandisinsignificantcomparedtothespeedofsound.

NotethatGalileotriedtomeasurethespeedoflightusingasimilarmethod.Lightmovessoquickly,however,itrequires

extremelylargedistancestomeasurethetimeittakestotravelusingastopwatch.RatherthansayingthatGalileofailedin

hisattempt,weliketosayhesucceededinprovingthatlightwasmuchfasterthanhecouldmeasure.

OtherThingstoTry

Thedistance toa lightningstrikecanbedeterminedbycounting thenumberofsecondsbetweenseeing the lightingand

hearingthethunder.Usingaknownvalueforthespeedofsoundmultipliedbytimecanprovideanestimateofthedistance

tothelightningstrike.Similarly,thespeedofsoundcanbedeterminedifthedistancetothelightningstrikeisknown(orcan

bemeasured, suchasbydriving towhere the lightningwasobserved tohit) anddividedby the timebetweenseeing the

lightningandhearingthethunder.

ThePoint

Speedisdistancedividedbytime.However,theaccuracyofanyexperimentislimitedbytheresolutionoftheleastcertain

measurement.Evenifdistancecanbemeasuredaccurately,thetimemeasurementsarelimitedbythereactiontimeofthe

observer.

249

Project73

Speedofsound.Resonanceinacylinder.

TheIdea

Inthisexperiment,wemeasurethespeedofsoundbasedontheresonancethatatuningforkproducesoveracolumnof

water inacylinder.Unlike theverydirectapproachof theprevioussection,we takeadvantageof thewavepropertiesof

soundtomakeamuchmoreaccuratemeasurement.

WhatYouNeed

tuningforkofknownfrequency

rubbermallet

closedwatertightcylinder(about15–20cmtall)—a1–2Lgraduatedcylinderwillwork

ruler

200mLbeaker(orothercontainerwithaspouttopourwaterintothegraduatedcylinder)

water

quietroom

Method

1. Strike the tuning fork with the rubber mallet. Hitting the tuning fork on a hard surface may result in altering its

frequency.

2.Holdtheringingtuningforkoverthetopofthegraduatedcylinder,asindicatedinFigure73-1.

3.Placeyourearnearthetopofthegraduatedcylinderandlistentothesoundofthetuningfork.

250

Figure73-1Findingthecolumnlengththatresultsinresonanceataparticularfrequency.

4.Slowlyaddwater to thecylinderandcontinue to listen.This canbea several-personoperation.Becareful not to

causethewatertosplash,whichcandistractthelistenerfromhearingthesoundofthetuningfork.

5.Atacertainheight,asthewaterlevelisraised,thesoundofthetuningforkbecomesmarkedlylouder.Youmayneed

tolistencarefullytohearit.

6.Onceyouthinkyoufoundtheresonance,pouroutsomeofthewaterandconfirmthatthesoundlevelforthetuning

forkbecomeslower,andthengetslouderagainasthewaterlevelisbroughtbackup.Itshouldalsogetlowerasthe

water level is raisedabove the resonance level. (If youmiss the first resonance,continueaddingwaterandyouwill

hearthesecondresonance.Usingthewavelengthforthesecondresonancewillresultinaspeedofsoundthatishalf

thecorrectvalue.)

7.Determinethefrequencyofthetuningfork,eitherbynoticingthemarkingonthetuningforkorbymeasuringit.You

canuseaninstrumenttunertomeasureorverifythefrequencyofthetuningfork.

8.Calculatethespeedofsoundusingthisequation:

v=4Lf

whereListhelengthoftheaircolumnabovethewaterandfisthefrequencymarkedonthetuningfork.

9.Amoreexactexpressionwhichaccountsforthenodeofthesoundwavenotbeingexactlyattheopeningofthetube

ofdiameter,d,is:

251

v=4f(L+0.4d)

ExpectedResults

Theacceptedvalueforthespeedofsoundat20°Cis343m/s.Thewarmertheair,thefasterthespeedofsound,accordingtotheequationv=331m/s+0.6TwhereTisthetemperatureindegreescentigrade.

Togetan ideaof theappropriate height needed in the resonantair column for variouscommon tuning forks, youcan

check the following table. These values do not include the correction factor used in the experiment to account for the

diameterofthecylinder.Itispossiblethatsomeonedoingthisexperimentmaynotnoticetheresonanceofthefundamental

frequencyandwillcontinuefillingthegraduatedcylinderuntilarrivingattheresonanceforthesecondharmonic.Table73-1

servesasaguidetofindthecolumnheightthatproducesaresonantfrequency.

WhyItWorks

Theresonanceoccurswhenthelengthofthecolumnproducesanaturalresonancethatisthesameasthetuningfork.

Table73-1

Onewaytothinkaboutthisisthat,atthespeedofsound,thesoundgoestothebottomofthecolumnandbackinthe

sametimeasthetuningforkgoesthroughonevibration.

Anotherwaytosaythisisthefrequencyofthestandingwavethatresonatesequalsthefrequencyofthetuningfork.The

waveequationstatesthatthevelocityofawaveequalsitswavelengthtimesitsfrequency.Theequationis

v=λfwherevisthevelocity(inm/s),λisthewavelength(inm),andfisthefrequency(incyclespersecondorHz).

OtherThingstoTry

Comparethismethodtotheothermethodsofmeasuringthespeedofsoundfoundinthisbook.

ThePoint

The speed of sound can be determined bymeasuring the length of an air column at which a tuning fork establishes a

resonance.One-quarterwavelengthfitsintheaircolumn.Measuringtheaircolumncanthendeterminethewavelengthofthe

sound.Thiscombinedwiththefrequencydeterminesthespeedofsound.

252

Project74

Racingagainstsound.Dopplereffect.

TheIdea

WeatherforecastersusetheDopplereffecttodetectwindshear.Astronomersuseittodeterminethatdistantgalaxiesare

movingawayfromeachotherinanapparentexpansionoftheuniverse.Thisexperimentdemonstrateshowthefrequencyof

asoundmovingtowardorawayfromalistenerisaffectedbytheDopplereffect.

WhatYouNeed

1meterlengthofstring

1electricbuzzerorothersourceofasustainednote(thebuzzermusthaveapointofattachmentforapieceof

stringandmustnotrequiresomeonetocontinuouslyactivateaswitchtomakeitsound)

2people

optional:microphone,oscilloscope,orsoundcardoscilloscope

Method

1. Securelyattachthebuzzertothestring.

2. Turnonthebuzzer.

3. Onepersonspinsthebuzzerinacircle,movingtowardandawayfromthesecondperson,asshowninFigure74-1.

4. The observer should listen to the sound the buzzer makes as it comes toward and away from where they are

located.

ExpectedResults

Thepitchofthesoundincreasesanddecreasesatarateestablishedbytheperiodoftherotatingbuzzer.Thevolumeofthe

buzzersoundmayalsoincreaseanddecrease,butthatisnottheDopplereffect.Thefasterthebuzzerspins,thegreater

thedifferenceinpitch.

Thepitchishigherasthesoundmovestowardyouandlowerasitmovesawayfromyou.

WhyItWorks

Whensoundiscomingtowardyou,thepeaksandtroughsofthewavesareclosertogether,asindicatedinFigure74-2.This

resultsinahigherfrequencyofthesoundwave.Fromtheperspectiveofthelistener,thesoundwavesseemtocomemore

frequentlyandareperceivedtohaveahigherpitch.

OtherThingstoTry

Attachthemicrophonetoeitheraphysicaloscilloscopeorasoundcardoscilloscope.Displaythesoundandcomparethe

frequencyproducedbythebuzzercomingandgoing.

253

Figure74-1Soundvariesinpitchasitmoveswithrespecttothelistener.

Figure74-2Asthebuzzermovestowardthelistener,theperceivedpitchofthesoundishigher.Asitgoesaroundthecircle

andmovesawayfromthelistener,thepitchbecomeslower.

Attachabuzzertoanyobjectthatcanmoveinamoreorlesshorizontaldirection(suchasanairtrackglider,africtionless

cart,orevenanoldskateboard).Astheobjectmoves,listentothesound.Ifyoucan,alsotrydisplayingthewaveformonan

oscilloscope.

ThePoint

TheDopplereffectoccurswhenthesourceofthesoundiseithermovingtowardyouorawayfromyou.Whenthesourceof

soundismovingtowardyou,thepitchorfrequencyofthesoundishigher;whenthesourceofsoundismovingawayfrom

you,thepitchislower.

254

Project75

Addingsounds.Beatfrequency.

TheIdea

Whenwavesmeetupatthesamepointinspace,thewavesaddtogethertoformanewwave.Thiscombiningofwavesis

calledsuperposition.Thewavesaddtogetherinaprocesscalledinterference.Ifthecrestsformatthesameplace,wehave

constructiveinterferenceandthecombinedwaveissmaller.Ifacrestmeetsatrough,wehavedestructiveinterferenceand

asmallerwave.

Sometimeswhenwavescombine,thepatterntheyproduceisitselfawave.Wecanhearthebeatfrequencyofasound

wavemosteasilywhentwosoundwavesareseparatedbyasmallfrequencydifference.

WhatYouNeed

sourceoftwotonesthatdifferbyafewHz.Someoptionsforthisinclude:

–adjustabletuningforkpairwithresonantcavities

–2matchedtuningforks,oneofwhichcanbedetunedbyapplyingasmallmasstothetinesofoneofthetuningforks

–(Polyphonic)keyboardsynthesizer

waveformgeneratorwithtwochannelsortwowaveformgenerators

optional:agoodpairofears

optional:anoscilloscope—eitheraphysicalinstrumentorasoundcardoscilloscope

Method

1. PlaytwotonesatthesametimethataredifferentbyonlyafewHz.Forinstance,youcanuse440and445Hz.Or,

youcanplaytwonotesonakeyboardseparatedbyasteportwo.

2. Listencarefully.Seeifyoucandistinguishthefirsttoneandthesecondtoneindividually.Then,listenforafadingin

andoutoftheoverallsound.Thatthrobbingofthebasictoneiscalledthebeatfrequency.Thepulsationitselfhasa

frequencyequaltothedifferencebetweeneachofthetwoindividualfrequencies.

3. UsingthetechniquedevelopedinProject64,displaythecombinedwavesforeachofthetonesontheoscilloscope.

4. Measure the frequency of the overall pulsating wave pattern that envelops both waves. Compare that to the

differenceinfrequencyforeachofthetwoindividualwaves.

ExpectedResults

Youshouldhearapulsatingthrobbingtonethatcausesthecombinedtonestoperiodicallygrowlouderandsofter.

Asanexample,bycombininga440Hzwavewitha445Hzwave,yougetacombinedtonethatgetslouderandsofter

everyfiveseconds,asshowninFigure75-1.Thebeatfrequencyisthedifferencebetweenthetwooriginalwaves.

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Figure75-1Additionoftwofrequenciesproducesabeatfrequency.

WhyItWorks

Whentwowavesareproducedatthesamelocation,thebeatfrequencyequalsthedifferencebetweenthefrequenciesof

thetwowaves.

OtherThingstoTry

Wecanalsolookattheproductofthetwowavesthatexaggeratestheoverallpatternofthebeatfrequency,asshownin

Figure75-2.Manyoscilloscopesdisplaytheproductofthetwoinputwaveforms.

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Figure75-2Multiplyingtheamplitudesoftwosoundwavesshowsthebeatfrequencymoreprominently.

ThePoint

Thebeatfrequencyisthedifferencebetweenthefrequenciesofthetwoindividualwaves.

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Project76

Pendulumwaves.

TheIdea

Thisdemonstrationusesanapparatusbuilt fromseveraldifferentmasseshanging fromstrings.Eachpendulum isslightly

shorterthanitsneighbor.Becausetheperiodofapendulumislongerforlongerstring,eachpendulumwillgobackandforth

inslightlylesstimethanitsneighbor.Thisdifferenceresultsinanoverallchangingpatternofstandingwavesandtraveling

waves.

WhatYouNeed

8–12smalluniformmasses(nuts,hookedmasses)

stringorfishingline

frame,asshowninFigures76-1and76-2,whichallowsthestringforeachsuccessivemasspendulumtobecome

progressivelylarger

ThisapparatusisalsocommerciallyavailablefromEdmundsScientific(itemnumber3123752).

The followingequation (fromPendulumWaves:ThePhysicsofaSetofTunedPendulums, BradDeGregorio, found at

member.cox.net/brad.degregorio/PendulumWave.pdf)givestheoptimallengthsforeachpendulumstring:

Lengthofnthpendulumstring:

where,Tmaxistheperiodofthelongestpendulum,kisthenumberofcyclestheapparatusgoesthroughbeforerepeatingits

pattern,andnisthenumberofthependulum(n=1isthefirstpendulum,n=2isthesecond,andsoon).

Figure76-1Invertedstaircaseframeforpendulumwave.

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Figure76-2Simpleframeforpendulumwave.

Table76-1

Table76-1givesthelengthofasetofstringsforapendulumwavetorepeatevery30secondswith25oscillationsforthe

longeststringduringthattime.

Noticethattheoptimalstringlengthisnotlinear.Somependulumwaveframesareactuallycurvedtoaccommodatethe

shapegivenbythepreviousequation.

Method

1. Attachthestringstothemasses.

2. Adjustthestringlengthsbetweenthemassesandtheframe,soallthemassesarethesamelength.

3. Attachtheotherendofeachstringtotheframe,soeachofthemassesisatthesameheightfromtheground.The

massesshouldbelowenoughsotheycanbeobservedfromabove.

4. Securetheframetoatableorothersupports,soeachofthemassesisfree-swingingabovethefloor.

5. Holdallthemassesandpushofftoonesideusingameterstickorflatboard.Themassesarenotpushedtoward

eachother.

6. Release themasses and observe from above. Placing a board underneath themassesmay help in viewing the

patterntheyformastheymove.

ExpectedResults

Themassesdefineacontinuouslychangingpattern.Withthefirstswing,themassesallswingprettymuchtogether,resulting

inthepatternsshowninFigures76-3,76-4,and76-5.

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Figure76-3Linearalignment.

Figure76-4Quarterwave.

Figure76-5Fullwave.

WhyItWorks

Theperiodofapendulum,orthetime,T(inseconds),ittakestoswingbackandforthonetimeincreaseswiththelengthof

thependulum,accordingtotheformula:

T=2π(L/g)½

whereListhestringlength(inmeters)andgisthegravitationalaccelerationconstant(inm/s2).

Becauseeachsuccessivemasshasaslightlylongerstring,itsperiodislongerthanthemassbeforeit.Themorecycles

themassesgothrough,themoredifficultitisforthemassesonthelongerstringstokeepup.Thedelaythatoccursinthe

slowermassesbeginstodevelopintothepatternsdepictedinthepreviousfigures.

OtherThingstoTry

A follow-up to thisexercise is topredict theperiodduringwhichasequenceofpatterns repeats.Thiscanbeverifiedby

measuringhowoftenaparticularpatterntakestorecurcomparedwiththestepsizeforeachsuccessivependulum.

ThePoint

This project illustrates the variability of the period of a pendulum with string length. It also shows how changes in the

frequencyofawavecanhaveaneffectonwhetheritisinphaseoroutofphasewithothermassesinthesystem.

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Project77

Usingwavestomeasurethespeedofsound.

TheIdea

Inthisexperimentyouwilldeterminethespeedofsoundbymeasuringhowlongittakessoundtogetfromonemicrophone

toanotherseparatedbyaknowndistance.ThisisalmostthesamethingyoudidinProject72.Theonlydifferenceisthat

hereweuseanoscilloscopetomeasurethedifferenceintimeinsteadofastopwatch.

Youcantakeadvantageofthewavepropertiesofsoundtofindthedistancebetweenthepositionswherethesoundis

loudest.Thisoccurswherethesoundconstructivelyinterferes.Thisletsyoufindthewavelengthofthesound.Knowingthe

wavelengthandfrequencyofsoundletsyoudetermineitsvelocity.

Thisexperimentprovidesanopportunitytoexplorebasicpropertiesofwavesingeneral.Theoveralltechniquesusedhere

can,withsignificantrefinements,alsobeusedtomeasurethespeedoflight.

WhatYouNeed

2speakers

2approximately6-footlengthsofhookupwire

tonegeneratororasingletonewavfileplayedthroughacomputerordigitalaudioplayer

2microphonesconnectedtoanoscilloscope(orasensitivesoundmeter)

tapemeasure,meterstick

quietroom

Method

Twospeakers/onemicrophone

1. Connectthetonegeneratortothetwospeakersusingthehookupwire.Connectthepositiveterminalofthetone

generatortothepositiveterminalofeachofthespeakers.Thenegativeterminalofthetonegeneratorisconnected

tothenegativeterminalsofeachofthespeakers.

2. Positionbothspeakersside-by-sidedirectedtowardthemicrophone.Atthispointandthroughoutthismeasurement,

eachspeakershouldhaveanunobstructedline-of-sightviewtothemicrophone,asshowninFigure77-1.

3. Turnon the tonegenerator.Verify thatbothspeakersarefunctionalandat roughly thesamevolume.Youshould

hearasteady,continuoustone.Anymidrangerangefrequencyshouldwork,suchas440Hz,althoughthismethod

workswellforallaudiblefrequencies.

4. Connect themicrophone toyouroscilloscope. (Alternatively, youcanuseasoundmeteror just listencarefully to

determinethepositionsofmaximumandminimumsoundintensity.)

5. Display thewaveformpickedupby themicrophoneson theoscilloscope.Adjust theamplitude, timescale,and, if

needed,thetriggersetting.

6. Slowly move one of the speakers (either forward or back) along the line between it and the microphone. Each

speakershould,atalltimes,continuetofacethemicrophone.

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Figure77-1Findingthedistancebetweenpositionsofmaximumintensitytodeterminethespeedofsound.

7. Monitortheamplitudeofthesignaldisplayedontheoscilloscope(ortheintensityonthesoundsensor;youcanalso

heartherelativeintensityofthesoundwithreasonableaccuracy).Becarefultoavoidanyobjectsthatcouldblockor

reflectthesoundwavesstrikingthemicrophone.

8. Notethefrequencyofthesoundwaves(fromthesettingonthetonegeneratororthewavfileyouused).However,if

youdon’tknowthefrequency,orjustwanttoconfirmit,determinehowmanysecondsittakesonthetimescalefor

onefulloscillationtooccur.Thetimeittakesforonewavelengthtooccuriscalledtheperiodofthesoundwave.

Thereciprocaloftheperiodisthefrequency,f(inHzorcyclespersecond).

9. As you adjust the distance between the speakers, you should see the amplitude of the combined sound waves

decrease,reachaminimum,andthenreturnbacktoitsmaximumlevelasthespeakersaremoved.

10. Thedistance between the speakerswhen the sound is at amaximum is a fullwavelength. This is the result of

constructivereinforcementofthesignals.Thedistancebetweenthespeakerswhenthesoundisataminimumisa

halfwavelength,resultingindestructiveinterference.(ThecomponentsforthisexperimentareshowninFigure77-2.)

Figure77-2Componentstomeasurethespeedofsound.

11. Measure the distance between the two speakerswhen the sound is atmaximum level. This distance is one full

wavelength,λ,ofthesoundwave.Ifyoumeasurethisinmeters,yourcalculationforthespeedofsoundwillbeinmeters per second. (You can get additional data points by measuring different locations, finding the one-half

wavelengthfromthepositionswhenthesoundisataminimum,andthenrepeatingthisatvariousfrequencies.)

12. Oncewehavethewavelength,λ,andthefrequency,f,youcanmultiplythemtogethertogetthevelocityusingthewaveequation:

v=λf

ExpectedResults

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Asbefore,thespeedofsoundat20degreescentigradeis343meterspersecond.

Thespeedofsound(inmeterspersecond)asafunctionoftemperature(indegreescentigrade)isv=331+0.6T.

Usinga440Hz tone, thedistanceseparating themicrophones togeta343meterper second value for thespeedof

soundis0.78meters(78centimeters).

A1000Hztonewouldrequirea0.343meterseparationtoresultintheexpectedvalueforthespeedofsound.

WhyItWorks

Twowavestravelinginthesamedirectionaddtogethertoformanewwave.Ifthecrestsofthetwowavesriseatthesame

time and place, the waves are said to be in phase and reinforce each other to produce a louder sound. This is called

constructiveinterference.Thisoccurswhenthetwosourcesofthesoundareseparatedbyexactlyonefullwavelength.(One

wavegetsaone-wavelengthheadstart,butbothareinphaseatthedetector.)Ifweknowthewavelengthandthefrequency

ofthesound,wecaneasilydetermineitsvelocityaccordingtotherelationshipv=λf.

Figure 77-3 Sound waves (amplitude versus time) shifted by one-half a wavelength as a result of traveling through the

distancebetweenthetwospeakers.

Destructiveinterferenceoccurswhenonewavecrestswhilethetroughofasecondwaveispassing.Thishappenswhen

thesourceofthetwowavesisseparatedbyhalfawavelength.

OtherThingstoTry

Twomicrophones/onespeaker

If you can set up two microphones to your oscilloscope, there is another way to do this that shows the process of

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interferencemoreclearly. Inthiscase,youfollowbasicallythesameprocedureasthepreviousone,exceptyouhaveone

speakerandtwomicrophones.Youmovethemicrophonesuntilyouobservedestructiveinterference.Thisoccurswhenthe

crestofonewaveisatthesameplaceasthetroughoftheotherwave,asshowninFigure77-3.Thismethoddoesnotwork

usingasoundintensitymeterorbylisteningcarefully,asdidthepreviousmethod.

Followingthismethod,youcanusethecapabilitythatmanyoscilloscopeshavetodetectthepointatwhichthewavesare

separatedbyone-halfawavelength.Thisinvolvesplottingonesignalversustheotheronthedisplay.Whenthisxversusy

plot isastraight linewithaslopeequal toanegativeone,asshown inFigure77-4,yoursignalsare180degreesoutof

phaseandseparatedbyone-halfwavelength.

Figure77-4x–yplotoftwosoundwavesshowingtheseparationofone-halfwavelength.

Interferencealongaline/doubleslitanalogy

AnotherconfigurationthatcanbeusedtofindpositionsofaconstructiveanddestructiveinterferenceisshowninFigure77-

5.ThismethodisanalogoustothedoubleslittechniqueusedbyThomasYoungwithlightandisexploredinProject83.The

wavelengthisgivenby:

λ=dsinθwhered is theseparationbetween thespeakersandθ is theanglebetween themidpointbetween thespeakersand thepointwhereconstructiveinterferenceisidentified.

Speedoflight

Usingasimilarprinciple, thespeedof lightcanalsobemeasured in the lab.Anapparatus iscommerciallyavailable that

determines the wavelength of a known frequency of light by measuring the distance between positions of constructive

interference. Themeasurement is much trickier than the one in this experiment because the speed of light is somuch

greaterthanthespeedofsound.Thesamebasicapproach,however,canbeappliedtoeithersoundorlight.

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ThePoint

Thespeedofsoundcanbedeterminedifthewavelengthandfrequencyofthewaveareknown.Thewavelengthforagiven

frequencycanbedeterminedbyfindingthedistanceatwhichconstructiveinterferenceoccurs.

Figure77-5Findingthelocationsofmaximumandminimumsoundintensitytodeterminethespeedofsound.

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Section7

Light

Project78

Rayoptics.Tracingthepathoflightusingalaser.

TheIdea

Thisisaperfectwaytoseeforyourselfhowlightmoveswhenitencountersmirrorsandlenses.

WhatYouNeed

laserpointer

setoflenses,includingconvex,concave,rectangular,andsemicircularlens;rectangularprismand60andright-angle

prisms(90°,45°,45°)and(90°,30°,and60°)2smallflatmirrors

sheetofpaper(plainorgridded)

ruler

protractor

darkroom

Method

1. Caution—Youshouldusealow-powerlaserpointerandbecarefulnottoshinethelaserwhereitcouldhitanyone’s

eyes.Remember,youareworkingwithopticaldevicesthatchangethepathofthelight,sobecarefultoavoidstray

lightraysthatcouldaffectanyone’seyes.

2. Placeyourobjectlens(ormirror)onaflattable.

3. Placeasheetofpaperunderneaththelens.

4. Tracetheoutlineofthelensonyourpaper.Leaveenoughroomtodrawincomingandoutgoinglines.

5. Darkentheroom.

6. Shinethelaserataslightangle,soitsstraightlinepathcanbeseenonthepaper.

7. Foreachofthelenses,putthreeormoredotsalongthepathtodefinetheincidentpath.

8. Observeitspaththroughthelens(orreflectedfromthemirrors).Youmayneedtoslightlyadjusttheangle(tothe

planeofthetable)tomakethetransmittedrayvisible.Dependingonyourlenses,youmaynotbeabletoseethe

laserlightgoingthroughthelens.Also,becarefulnottomistakelightthatmaysneakunderneaththelensasaray

that follows the intended optical path through the lens. Also (again depending on your lenses), youmay need a

slightlydifferentangletomaketheincidentlaserlinevisibleasyouwouldneedfortherefractedline.Ifthisisthe

case,makesureyoucomeintothelensalongthesameincidentlinethatyoudrew.

9. Makethreeormoredotstodefinetherefracted(orreflected)paths.

10. Makeadotwherethelightentersthelensandwhereitleavesthelens.

11. Connectthedotswithstraightlinesshowingtheincident(incoming)line,thestraightlinethroughthelens(whichis

therefractedline),andthetransmittedorreflectedlines.

12. Exploreasmanyofthefollowingopticalobjectsasyouhaveavailable.Thefollowinglistsseveralspecificthingsto

focuson.

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(Note:Allthiscanbedone,ifyouprefer,onamagneticchalkboardusinglenseswithmagneticbacks.Youcaneitherglue

strongmagnets toyour lensorsimplyhold the lens to thechalkboard.Makesure that themagneticchalkboard isstrong

enough to hold the lens securely and that themagnet does not block the path of the light. Laser levelsmay be useful

becausetheyhavebuilt-inanglestomakethelinevisiblealongasurface.However,theymaybealittletrickiertofocusall

thewaythroughthelens.)

Singlemirror

Drawaperpendicular linetothesurfaceofthemirror.Shinethe laseratthepointwheretheperpendicular linemeetsthe

mirror.Placedotsalongtheincidentlineandthereflectedline,andthenconnectthedots.Comparetheincidentanglewith

thereflectedangle.Trythisforseveralsetsofangles(Figure78-1).

Mirrorsatarightangle

Shine the laserononeof themirrorsand trace itspath (byplacingdotsalong thepathandconnecting them).Thepath

shouldhitthesecondmirror,andthenreflectoffthesecondmirror.Trythisforseveralanglesofincidenceonthefirstmirror.

(Ifyoulikegeometry,setthemirrorsatanacuteangle.Then,predictandtesttheangleoftheoutgoingrayforagivenangle

ofincidence.)

Figure78-1Reflectionfromaplanemirror.

Convexlens

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Aconvexlensistheonethatisthickeratthemiddlethanattheends.Drawacenterlineperpendiculartotheaxisofthelens.

Tracethefollowingpaths:a)astraightlinealongthecenterlinethroughthecenterofthelens,b)alineabovethecenterline

runningparalleltothecenterline,c)alinebelowthecenterlinerunningparalleltoit.Traceallthelines.Noticewherethethree

linescross.Measurethatdistanceandputadotonthecenterlineontheincidentsideofthelensthatsamedistancefrom

thelens.Directthelaseratanyanglethroughthatdotandtraceitspaththroughthelens.Trythisforseveralangles.

Figure78-2Mirrorsatarightangle.

Figure78-3Convexlens.

Concavelens

Aconcavelensistheonethatisthinneratthemiddlethanattheends.Drawacenterlineperpendiculartotheaxisofthe

lens. Trace the following paths: a) straight line along the center line through the center of the lens, b) a line above the

centerlinerunningparalleltothecenterline,c)alinerunningbelowthecenterlinerunningandrunningparalleltoit.Traceall

thelines.Howdotheseresultscomparewiththosefromtheconvexlens?

Semicircularlens

Thesemicircularlenshasonecircularsideandoneflatside.Placethecircularsidetowardyou.Tracethelensanddrawa

268

centerlineon the flat side.Shine the laserat a30-degreeangle to that centerline, but hit thepointwhere thecenterline

meets the flat side of the lens. This particular arrangement avoids refraction in the glass because the light comes in

perpendiculartothetangentatthecircularedge.Inthiscase,theonlyrefractionthatoccursisattheglass-to-airinterface.

Observewhathappensfordifferentangles.Takeittotheextremesofhighandlowanglesofincidence.

Figure78-4Concavelens.

Figure78-5Semicircularlens.

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Figure78-6Rectangularprism.

Rectangularprism

Drawaperpendicularlinetooneoftheedgesoftheprism.(Makesuretheedgesyouareusingareclearandnotfrosted.)

Directthebeamtowardthepointwheretheperpendicularmeetstheedgeandtracethepathofthelaserthroughtheprism

atvariousangles.

Right-angleprisms

Therearetwomaintypesofright-angleprisms:90°,45°,45°and90°,30°,60°.Hereisachallenge.Tryiteitherbyworkingoutthelightraysfirstorbyjustplayingwiththeprismsandfiguringitoutbytrial

anderror:

a)Howcanyoudirectalightraythroughtheprismandhavearayemergeat90degreestotheincomingray(basedonly

ontotalinternalreflection)?

b)Howcanyoudirectalightraythroughtheprismandhavearayemergeat180degreestotheincomingrayheading

backinthedirectionthatitcamefrom(alsobasedonlyontotalinternalreflection)?

ExpectedResults

Singlemirror

Themeasurementsshouldvalidatetheideathattheangleofincidenceequalstheangleofreflection.

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Figure78-745-degreeprism.

Mirrorsatarightangle

Regardlessoftheangleatwhichthelaserraystrikesthemirror,therayreflectedfromthesecondmirrorwillbeparallelto

theincomingray,butheadingintheoppositedirection.

Convexlens

Raysstriking the lens travelingalong thecenterlinewill gostraight through the lenswithoutbeingdiverted.Rays traveling

paralleltothecenterlinebendtowardthecenterlineandcrossatapoint(calledthefocalpoint)ontheoppositesideofthe

lens.

Figure78-860–30right-angleprism.

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Rayspassingthroughafocalpointonthesamesideofthelensasthelaser(samedistanceasthefocalpointmeasured

previously)emergefromthelensparalleltothecenterline.

Concavelens

Nomatterwheretherayshitthelens,theraysdonotcross.Abovethecenterline,theraysbendup.Belowthecenterline,the

raysbenddown.

Semicircularlens

Rayshittingthesemicircularsideanddirectedtowardthecenterofthecirclebend(orrefract)onlywhenemergingfromthe

glasstotheair.

Rectangularprism

Raysemergingfromthelensareparalleltotheincidentray,butoffsetinthedirectionthatraysmovethroughthelens.As

withalltheseobservations,thepaththeraytakesintheprismisastraightline.

Right-angleprism

Raysstrikingoneofthetwoshorteredgesofthe(90°,45°,45°)prismmakea90-degreeturn,andthenreflectback.Raysstrikingthelonger(hypotenuse)edgeofthe(90°,30°,60°)prismmakea180-degreeturn,andthenreflectback.

60-degreeprism

Theseproducearangeoftransmittedanglesandconditionsfortotalinternalreflection.

WhyItWorks

Lenses are optical devices that refract light passing from onemedium (air) through another (glass or plastic), and then

typicallybacktotheair.Ateachinterface,thelightisbentaccordingtoSnell’slaw.

Mirrors,whetherinvolvingoneormanysurfaces,reflectlightinsuchawaythattheangleofincidenceequalstheangleof

refraction.

OtherThingstoTry

Thelensesandmirrorspreviouslydescribedcanalsobestudiedusingthefollowingadditionalmethods:

Ray tracing with split beam. You can make or buy an apparatus that projects several parallel beams of light.

Basically,theapparatusconsistsofabulbcoveredbyanenclosurethatshinesthroughparallelopeningsintheside

of theenclosure.Thebeamsof light,whendirectedat thevarious lensesandmirrors,showthepropertiesof the

devicesinagraphicandintuitiveway.Thisapproachisbettersuitedtosmallerlensesandmirrors.

Ray tracing by locating images. Amore traditional approach is to view a vertical object such as a pin or a nail

through the lens.This isaccomplishedby:a) tracing theoutlineof the lens,b) locating thepositionof the image

seenthroughthelens,andc)drawingalinetoshowtheincident,refracted,andtransmittedpathsoflight.

ThePoint

Lensesandmirrorsdivert light inpredicableways.Lensesarebasedon refraction,whilemirrorsemploy reflection.Some

lensesareconverginganddirect raysof lightpassing through themthrougha focalpoint.Other lensesaredivergingand

directtheraysoflightinsuchawaythattheynevercross.Thereflectionatthesurfaceofanyplanemirroroccursinsucha

waythattheangleofincidenceequalstheangleofreflection.

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273

Project79

Twocandles,oneflame.

TheIdea

No, this is not the title of a bad country western song. This is a great optical illusion that is best shown to a group of

observerswhohavenothadthebenefitofseeinghowitwassetupbeforehand.

WhatYouNeed

2nearlyidenticalcandles

matchorlighter

table

paneofglass(orPlexiglas)

waytoholdtheglassperpendiculartothetablesafelyandsecurely.Thisworkswithsomeonesimplyholding the

paneofglassonthetable.Aringstandwithabeakerclamp(ortwo)alsoworkswell.

Method

Setup

1. Securetheglassperpendiculartothetable.

2. Placeonecandleonthetableintheuprightpositionononesideoftheglass.

3. Placetheothercandleuprightonthetableontheothersideoftheglassalongthesamelineandthesamedistance

asthefirstcandle.

4. Pickonesideoftheglasstoview.

5. Lightthecandleontheviewingside.

Figure79-1PhotobyS.Grabowski.

Viewing

1. Allobserversshouldbeonthesideofthepanewiththelitcandle.

274

2. Observetheappearanceofbothcandles.

ExpectedResults

Youcanseethe imageof theflamefrombehindtheglass,superimposedonthewickof the (unlit)candle in frontof the

glass.

Figure79-2PhotobyS.Grabowski.

WhyItWorks

Whenlightstrikesatransparentsurface,suchasapieceofglass,someofthelightisreflected,whilesomeofthelightis

refractedandtransmittedthroughtheglass.Theimageoftheburningcandleinfrontoftheglassisreflected.Theimageof

thecandlewithoutaflamefrombehindtheglassistransmitted.Boththereflectedandtransmittedlightraysformimages

thatfallontopofeachother.Thiscreatestheillusionthatasingleimageexistsandthecandlebehindtheglassisburning.

Figure79-3PhotobyS.Grabowski.

OtherThingstoTry

Anotherwaytodothisistoreplacetheunlitcandlewithabeakerofwater.Thewaterlevelshouldbeabovethelevelofthe

candle.Thereflectedimageofthelitcandlecombinedwiththetransmittedimageofthebeakerofwatercreatestheillusion

thecandleisburningunderwater.

Asimilarillusioncanbecreatedbymultiplereflectionscreatingavirtualimagefloatingintheair.InFigure79-4,theimage

ofthespaceshuttleappearstobehoveringoverthedome.

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Figure79-4Illusionoftheshuttleappearstobefloatingintheair.

However,whenviewedfromaslightlydifferentangle,therealtoyshuttlecanbeseenatthebottomofthedome,producing

thevirtualimagealsopicturedinFigure79-5.

Thislookssoreal,itiscommonforobserverstoreachinandtrytotouchthevirtualimagetoconvincethemselvesitisnot

real.

ThePoint

Atransparentobject,suchasglass,canbothtransmitandreflectlightthatisincidentonit.Reflectedlightfollowsthelawof

reflection,wheretheangleofincidenceequalstheangleofreflection.

Figure79-5Therealtoyshuttleseenatthebottomofthedomeisthesourcesoftheillusion.

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Project80

Laserobstaclecourse.

TheIdea

Thisisasimpleandfunwayofexploringthelawofreflectionthatprovidesaninitialinsightintowhatisneededtoachieve

opticalalignment.Thisproject(whichIfirstheardfromTomMisniak)makesagoodteam-buildingactivityandcanbeused

asthebasisforafriendlycompetition.

WhatYouNeed

low-powerlaser(alaserpointerisfine)

apparatus(suchasatripod)tomountthe laserpointandhold it illuminatedandstationaryforasustainedperiod

(youmayneedtotapethelaserpointtokeepitonwithoutholdingit)

severalplanemirrors

smallwhiteboards

waytomountthemirrors,suchasringstandsandclampsormodelingclay

darkroom

timer

Method

Competition1(Roundrobin)

1.Caution:Becarefulnottoshinethelaserbeamatanyone’seyes.Althoughthepowerofthelasershouldbelow,itisa

goodideatotakecarenottoexposeanyone’seyes.

2.Distributeamirrorandassociatedmountinghardwaretoeachparticipant.

3.Drawatargetandmountitinalocationwhereeveryonehasaclearline-of-sighttoit.

4.Setupthelaserpointerinacentrallocation.

5.Placetheparticipantsatdifferentlocationsaroundtheroom.

6.Defineasequenceforthebeamtoreflectfromonepersontothenextand,finally,tothetarget.

7.Optional:darkentheroom.

8.Directthebeamtothefirstmirror.Usethewhiteboard,ifnecessary,to“capture”thebeam.

9.Optional:startthetimer.

10.Next,alignthepointerandthefirstmirrortomakethebeamreflecttothesecondmirror.

11.Continuefromonemirrortothenextuntilthelastmirrordirectsthebeamtothetarget,asshowninFigure80-1.

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Figure80-1Laserobstaclecourse.

12.Optional:incasethisgetstooeasy,requirethefinalbeamtopassthroughacardboardtubemountedinfrontofthe

target.

13.Compasses(forCompetition2).

Competition2:Backtothetarget

1. Takesimilarprecautions,distributemirrors,andestablishatarget,asinCompetition1.

2. Placetheparticipantsatdifferentlocationsaroundtheroom.

3. This time, however, have each participant work out their angles and alignment based on applying the law of

reflectionandmeasuringangles.

4. Giveeachparticipantasettime.

5. Whenthetime isup,allparticipantsmustno longer touchthemirrors. In fact,youcanhavethem leavethearea

altogether.

6. Thencomesthemomentoftruth,whereyouseehowcloseeachoftheparticipantsisabletodirectthelasertothe

target.

ExpectedResults

Itisnotunreasonabletohavesixreflectionsinabouttenminutes.Thisrequiresinteractionandcoordinationbetweengroups.

Onelessonpeopledoingthislearnisthatsmallchangesatthebeginningofthecourseresultinlargeerrorsattheend.Even

vibrationsinthefirstmirrorinthesequencecanthrowoffthealignmentdownstream.Adjustmentsmayneedtobemadeat

eachstep.Anothervaluablelessonistherecomesatimewhenitisbesttoleavethemirroraloneandstopmakingchanges.

Oneotherthingthatmaynotimmediatelybeobviousisthisisathree-dimensionalalignmentproblem.Younotonlyneedto

adjustleftandright,butalsoupanddown.

WhyItWorks

Thisisanapplicationofthelawofreflection.Becausethereflectionanglefromonemirrorbecomestheincidentangleof

thenextmirror,errorsinincidencedoublewitheachreflection.

OtherThingstoTry

278

Forthetrulydedicated:workouttheanglesformultiplereflectionsandbacktothetargetonpaperfirst.

ThePoint

The angle of incidence equals the angle of reflection. Small alignment errors can be quickly compoundedwhenmultiple

reflectionsoccur.

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Project81

Lightintensity.Puttingdistancebetweenyourselfandasourceoflight.

TheIdea

Weallknowthatstarsareintensesourcesoflight,buttheyappearasfaintobjectsintheskybecausetheyaresofaraway.

Howdoesthatwork?Ifyouincreasethedistancebetweenyourselfandalightsource,doesthelightbecomeone-halfofits

originalbrightnessordoesitdropoffsomeotherway?Checkitoutandseeforyourself.

WhatYouNeed

Alight-sensingcircuitassembledfrom

–solarcell

–insulatedwire(youneedtwo15-inchlengthswiththeinsulationremoved)

–wirestripper(apenknifeorapairofscissorswilldo)

–ammeter(ifyouhaveamultimeter,configureitasanammeter)

–solderingironwith(resincorePb/Sn)solder

–athirdhand(orasecondpersontohelpsolder)

oracommerciallyavailablelightmeter,suchasshowninFigure81-1

Figure81-1Lightsensor.CourtesyPASCO.

lightbulb(notafocusedsource,suchasalaserorflashlight)

tapemeasure

darkroom

Method

Attachingwirestoasolarcelltouseasasensor

1. Pluginthesolderingiron.Makesurethetipisinasafeplace.Itgetsveryhotinafewminutesandshouldnotbein

contactwithanybodyoranythingthatisflammable.

2. Placethesolarcellwiththebluesideupandlocateapadneartheedgeintendedforwireattachment.

3. Asthesolderingirongetshot,“wet”thetipbymeltingsomeofthesolderonthesolderingirontip.

4. Stripabout¼inchoftheinsulationfromtheendofeachoftwo15-inchlengthsofwire.

5. Positionthewireononeofthecontactpadsontheedgeofthesolarcell.

6. Positiontheendofsolderfromthecoilonthepadandnearthewire.

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7. Touchthesolderingirontothewiretogetitashotaspossible.Thismayhappenabitfasterifitisatfirstraised

abovethesolarcelltoavoidheatbeingconductedbythesolarcell.Youalsowanttoavoidoverheatingthesolar

cell,whichcouldcauseittoshortoutiftheheatisexcessive.And,youshouldavoidhavinganyelectricalcontact—

whetheritisthewiretouchingorsolder—betweenthefrontpadandthebackofthesolarcell.Thiscanshortoutthe

solarcellandpreventitfromgeneratinganelectricaloutput.

8. Touchthesoldertotheheatedwireand,asitmelts,havesomeofthemoltensolderformabridgetothesolder

pad.

9. Removethesolderingironanddon’tmoveuntilthesoldersolidifies.Ifdoneproperly,thesoldershouldsticktoboth

thesolarcellpadandthewireformingamechanicalbond.

10. Similarlyattachawireanywheretothebackofthesolarcell.

11. Attach thewire coming from the back of the solar cell to the positive terminal of the ammeter. Attach thewire

comingfromthefrontofthesolarcelltothenegativeterminaloftheammeter.

12. Atthispoint,youcan(carefully)holdthesolarcellormountitbygluingortapingittoaboard.Remember,solarcells

are extremely fragile and will break if the slightest pressure is put on them. The solar cell may still function if

fractured,butreasonablecautioncanavoidthat.

Makingthemeasurement

1.Positionthelightbulb,soafewmetersareinfrontofitwithoutobstruction.

2.Turnofftheroomlights.

3.Pickalocationsuchasabout25cmfromthelightbulbandtakeareadingonthelightmeter.(Thisstartingdistance

isarbitraryanddependsonthesensitivityofthemeteryouareusing.)

4.Recordthedistance(anychoiceofunit,inches,ormeterscanwork,butbeconsistentthroughoutyourinvestigation).

Recordthelightintensity,asshowninFigure81-2,intheunitsinwhichthelightmeteriscalibrated(suchaslumem/m2

lm/m2).

Figure81-2CourtesyPASCO.

5.Ifyouareusingthesolarcell,orientitsoitisperpendiculartothelinebetweenyouandthesourceoflight;theunitof

measurement will be in amps. Be careful not to block the front of the solar cell with your fingers, which can

compromisetheaccuracyofyourreading.

ExpectedResults

Thefartherawayyouget,thelessintensethelightbecomes.

Therateofdrop-offisnotlinear.Thefartherawayyouget,thefasterthelightintensityfallsoff.

Morespecifically,thelightintensitydropsoffastheinverse-squareofthedistance.ThisisshowngraphicallyinFigure81-

3.

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Figure81-3CourtesyPASCO.

WhyItWorks

Lightintensityisrelatedtothedistancefromitssourceaccordingtotheequation:

I=Io/r2

whereIrepresentslightintensityatdistance,r,betweenthelightsourceandthepointofmeasurementforaninitialintensity,

Io.

OtherThingstoTry

Asimilarinversesquarelawrelationshipcanbefoundwithasourceofsoundandasoundintensitymeter.

ThePoint

Lightintensitydropsoffastheinversesquareofthedistancefromthesourceoflight.

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Project82

Howdoweknowthatlightisawave?ThomasYoung’sdoubleslitexperimentwitha

diffractiongrating.

TheIdea

SirIsaacNewtonwasdefinitelynoslouchwhenitcametophysics.And,ifyouaskedNewtonwhetherlightwasawaveora

particle,hewouldsayitwasaparticle.Newtonwasactuallycorrectforreasonsthatwouldnotbecomeclearuntilseveral

centurieslater.ThomasYoungprovedtheoppositewastrue—thatlightwas(also)awave.Today,werecognizethatlighthas

bothparticleandwave-likebehavior.Were-createYoung’sexperiment in thisproject toexplore light’swave-likebehavior.

Youngobservedtheeffectoflightemergingfromtwosmallslitsinanopaqueplate.Insteadoftwoslits,youcreateasimilar

effectusingadiffractiongratingwhichletsyouexploretheeffectofdozensofopenings.

WhatYouNeed

diffractiongratingavailablefromscientificsupplycompanies,including

–Edmunds300130713,500lines/inchhttp://scientificsonline.com

–PASCOOS9127600lines/mm(15,000lines/inch)http://store.pasco.com

–FreyScientific155909972115,000lines/inchhttp://www.freyscientific.com

laserpointer

meterstick

rulerwithmetricdivisions(centimeters)

indexcard

darkroom

holderstosupportrulers

holdersforcard,diffractiongrating,andgrating

Method

Settingup

1. Mountthediffractiongratingwiththelinesorientedupanddown.

2. Mounttheindexcard,soitisparalleltothediffractiongrating.

3. Arrange themeterstick, so you canmonitor the distance between the diffraction grating and the screen as you

adjust this distance. (If it is convenient to set up, one possible approach is to attach the diffraction grating and

screen directly to the meterstick, and then determine the distance between them from the difference in the

readings.)Agoodstartingdistanceisseveralcentimeters.

4. Hold(orsecure)thelaserpointer,sothelaserbeamisdirectedperpendiculartothediffractiongrating.SeeFigure

82-1.

5. Darkentheroomandturnonthelaser.(Caution:Aswithanyprojectinvolvingalaser,usealow-powerlaser,suchas

alaserpointer,andbecarefultoavoidcontactwithanyone’seyes.)

6. You should see the path of the laser through the diffraction grating. The brightest spot is called the central

maximum.Drawaverticallinethroughthecentralmaximum.

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7. Oneithersideofthecentralmaximum,youshouldalsofindamuchdimmerspot.Thisiscalledthefirstorderline. (It

ismore likeaspot thana line inourcasebecauseweareusing light froma laser, rather than theverticalslits

originallyusedbyYoung.)

Figure82-1Apparatususedforthisproject.

ExpectedResults

Apatternofspotsisproducedtotherightandleftofthecenterline.Thesearetheresultoftheconstructiveinterferenceof

waves.Thisprovesthatlightisawave.Or,moreaccurately,inadditiontohavingparticle-likeproperties,lightisalsoawave.

Ifthedistancetothescreenisincreased,thedistancebetweenthebrightspotsalsoincreases.Thedistancebetweenthe

laserandthediffractiongratingshouldnotmatter,however,becausethelightstrikesthediffractiongratinginaperpendicular

direction,regardlessofhowfaritiscomingfrom.

WhyItWorks

Whenwavesmeet, if thecrestsoccurat thesame time, thewavesadd.This iscalledconstructive interference. If when

wavesmeetacrestandtroughcometogether,thewavescancel.Thisiscalleddestructiveinterference.

Interferenceisabasiccharacteristicofwaves.Thelight-anddark-spotpatternistheresultofinterferenceofthewaves

emergingfromtwoadjacentopeningsinthediffractiongrating.

OtherThingstoTry

Onceyoulocatethefirstorderbrightspots,youcantrytolocatethesecond,third,andpossiblyhigherorderlines.Thismay

requireaverydarkroom.

ThePoint

This project recreates one of the most significant experiments of the twentieth century in which Thomas Young

demonstrated that light is a wave. Interference patterns are a unique characteristic of waves. Because light in this

experimentexhibitsaninterferencepattern,itprovesconclusivelythatlightisawave.

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Project83

Howtomeasurethesizeofalightwave.

TheIdea

Lightisawave.Theinterferencepatterncreatedbyoverlappinglightwavesisdifferentfordifferentwavelengthsoflight.We

canusethistodeterminethiswavelength.

WhatYouNeed

diffractiongratingofknownseparationbetweenthelines

laserpointerofknownwavelength(low-costredlasersaretypically650–670nm,greenlasersareintherangeof

535nm)

apparatususedinthepreviousproject(includingameterstick,ruler,indexcard,andassociatedclampsandholders)

protractor

darkroom

Method

1.SetuptheapparatususedinProject81.

2.Determinethespacingbetween the linesof thediffractiongrating.Diffractiongratingsuppliers typically identify the

numberoflinesinagivendistance.Forinstance,ifadiffractiongratinghas15,000linesperinch,thespacingfromthe

center-to-centeroftherulelinesis1inch/15,000linesor0.000067inchesbetweenlinesor0.0026mbetweenlines.

3.Darkentheroom.(Caution:Aswithanyprojectinvolvingalaser,usealow-powerlaser,suchasalaserpointer,andbe

carefultoavoidcontactwithanyone’seyes.)

4. On either side of the central maximum, you should also find a much dimmer spot. This is called the first order

maximum.Withapencil,markthedistancetoeachofthefirstordermaxima.

5.Usingthemeterstickandprotractor,measuretheanglebetweenthepointwherethe laser lightpassesthroughthe

diffraction grating and the first order spot on the card.Measure both the angle to the right and to the left of the

centerline.Theangletotheleftandtotherightofthecenterspotshouldbeveryclosetoeachother.Repeatingthis

measurementandtakingtheaveragecangiveamoreaccuratevalue.

6.Iftheroomisdarkenoughandeverythingelseisworking,itislikelyyouwillbeabletoseethesecondand,possibly,

thethird-ordermaxima.NotethedistanceandsavethedatafortheOtherThingstoTrysection.

7.Repeatthisusingseveralcombinationsofscreendistance.

8.Thediffractiongratingequationis

whereλ(Greekletter“lambda”)isthewavelength(inmeters),nistheorderoftheband=1,2,3…Forthefirstorder,n=1,anddisthedistance(inmeters)betweenlinesonthediffractiongrating.

9.Usethisdatatabletoorganizeyourdata.Convertallyourdatatometers.Ifyourmeasurementsareincentimeters,

convertthemtometersbydividingby1000.

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10.Comparetheaveragewavelengthyoufindtotheexpectedwavelength.

11.Note,ifyoureallywanttonailthismeasurement,rememberthelinesthemselvestakeupsomeofthatdistance.The

distancebetweenthelines(whichiswhatwereallyneed)isslightlylessthanthecenter-to-centerdistancebetween

lines.Youcancalibrateforthisdiscrepancybyusingthepreviousdiffractiongratingwithalightsourcewithaknown

wavelength.Bymeasuringthedistancebetweencardandgrating,thelocationofthefirstordermaxima,andusing

theknownwavelength, youcansolve ford, thespacingbetween the lines.Although this gets you intoabit ofa

chickenandeggsituation,itdoesenablethemostaccurateresults.

ExpectedResults

Forcommonlyuseddiffractiongratings,theexpectedwavelengthcanbefoundbymeasuringabrightlightmaximumatthe

followingangle.

WhyItWorks

Thedistancebetweenthebrightspotsestablishedwhenlightofagivenfrequencypassesthroughadiffractiongratingcan

beused tomeasure thewavelengthofasourceof light. If thespacingof thegratingand thedistance to the imageare

known,thewavelengthcanbedetermined.

OtherThingstoTry

For simplicity, we only used the first ordermaximum. You can try the previousmeasurement also using the second and,

possibly,thethirdordermaxima.Thistechniqueshouldgivethesamewavelength,regardlessofwhichorderisbeingused,so

findingthesameorasimilarresultfromdifferentorderscangiveyouaconfirmationthatyouaredoingsomethingright.

Thespectralbreakdownof lightemittedbyahydrogenatomcanalsobedetectedusingahigh-sensitivity lightsensor,

suchasPASCOpartnumberPS-2176.AnexampleofthisisshowninProject120.

The optical tracks on aCDor the grooves on a vinyl recording are effectively diffraction gratings. Use the diffraction

gratingequationtofindoutthespacingofthetracksonaCDorrecord.Basically, thereflectionfromthecloselyspaced

tracksonaCDcangiveasimilarinterferencepattern,suchasthatproducedbytransmissionthroughadiffractiongrating.

Details canbe found inanarticle called “UsingaLaserPointer toMeasure theDataTrackSpacingonCDsandDVDs”

(www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p011.shtml?from…).

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ThePoint

Adiffractiongrating is a device that produces an interference pattern when a light is shined on it. If that light has one

frequency(orismonochromatic),suchasalaser,theinterferencepatterncantelluswhatthefrequencyis.Thiscapability

formsthebasisofmanyanalyticaltechniquesthatrequiremeasuringthefrequencyoflightwithgreatprecision.

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Project84

Thespeedoflightinyourkitchen.Visitingthelocalhotspots.

TheIdea

Lightisanelectromagneticwave.Becauseofitsextremelyhighspeed,it isdifficulttomeasurethespeedoflightdirectly.

Historically,astronomerssuchasO.Roemeruseddistancesonthescaleofplanetaryorbitstogetahandleonhowfastlight

traveledthroughspace.Inthisproject,youmeasurethespeedoflightrightinyourownkitchen.Thetechniqueissimilarin

principletotheapproachweusedinProject73wherewefoundthespeedofsoundbyfindingitsresonantwavelength.Here,

youuseamicrowaveoventoestablishastandingwavethatcanbeusedtoestimatethespeedoflight.

WhatYouNeed

microwaveoven

sheetsofslicedcheese,barsofchocolate,oraboutfiveeggs

sheetorplate to holdabove food itemswithout rotating in theoven—some ideas includea rectangularwoodor

plasticcuttingboard,arectangularPyrexbakingdish,arounddishthatfitsasclosewall-to-wallaspossible,ora

sheetofposterboardcuttosize.Obviously,remembernometalshouldgointhemicrowaveoven.

ruler

calculator

light,soyoucanseeinsidetheoven(theovenmayhaveanadequatelightbuiltin)

Method

1.Microwaveovensrotatetospreadoutthehotspotsintheoven.Inthisexperiment,wewanttodetectthesehotspots.

So,ifyourmicrowaveovenhasarotatingtray,removeitfromyourmicrowaveoven.

2.Putanonrotatingsheetorplateinthebottomofthemicrowaveoven.

3.Cover theplatewith themicrowavable food:cheeseslicesorchocolateslabs.The layershouldbeasuniformas

possible in thickness and composition. If you choose to use eggwhites, pour a thin layer into a suitable dish and

spreaditouttoformathin,uniformlayer.

4.Lookthroughtheglasswindowofthemicrowaveovenandstartthemicrowaveovenonthelowestavailablepower

setting.Usealightshiningfromoutsideifthathelpsyouobservewhatisgoingoninsidetheoven.Ifyoudon’thavea

window, you need to cook in increments. Becausemicrowavesdiffer somuch in power, you need to determinean

appropriateamountoftimetouseforthis:10to15secondsisagoodplacetostart.

5.Continuerunningthemicrowaveovenuntilyounoticethefirstsignsofmeltspotsorcooking.

6.Stopthemicrowaveovenandidentifythepatternofmeltspots.Unlessyouaresurethemicrowaveovenhasrunlong

enoughtoestablishaclearmeltspotpattern,donotmovethetrayintheovenyet.

7.Measure the center-to-center distance between adjacentmelts spots. An example forwhat you are looking for is

showninFigure84-1.

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Figure84-1Microwavestandingwavenodesareindicatedbyhotspotsinmeltedcheese.

8.Becauseone-halfofawavelengthfitsbetweeneachhotspot, thewavelengthsforthemicrowavesintheovenare

twicethecenter-to-centerdistancemeasured.

9.Lookfora labelorsearchonlineforthespecificmicrowavefrequencyused inyourmicrowaveoven. Ifyoucannot

easilyfindthisfrequency,youcanuse2450MHz,whichisthefrequencyatwhichmostcommercialmicrowaveovens

operate.

10.When you finish, you canmake grilled cheese sandwiches, s’mores, or egg-white omeletswith the leftover food

ingredients.

11.Calculatethespeedoflightusingtheequation:

c=λforspeedoflight=thewavelength/frequency

Forλusethewavelength(inmeters)fromtwicethecenter-to-centerhotspotdistance.Forf,use2450MHz,whichis2,450,000,000Hzor2.45×109Hz(unlessotherwiseindicatedonthemicrowaveoven).

ExpectedResults

Supposeyoufindtheaverageofthehot-spotdistanceis6cm.

Thewavelengthofthemicrowaveresonantinthemicrowaveovenis12cm.

Inmeters,thisis12cm×0.01m/cm=0.12m.Thespeedoflightisthen,c=0.12m×2,450,000,000Hz=2.94×108m/s.Thisisreasonablyclosetotheacceptedvalue,whichisjustunder3×108m/s(300,000,000m/s).Remember,microwaves

mayvaryinhowtheycreatestandingwavesandanerrorfactorisassociatedwithheatdistributionontheheatsurface.For

thisreason,thismeasurementcanbeonlyexpectedtogiveballpark,notpreciselyaccurate,values.

WhyItWorks

Amicrowaveovenproducesaresonantwaveintheovenchambersimilartothatofavibratingguitarstring.Thehotspots

arelikethenodesorthepointswheretheendsofthestringareheld.Acompletewaveisacycleupanddown,soonlyahalf

wave fits between the two nodes in both cases. From knowing the frequency of the microwaves and measuring its

wavelength,wecanfindthespeedoflight.

OtherThingstoTry

Amoresophisticated,butmoreprecisewaytomeasurethespeedoflightistodetecttheinterferencebetweenlightwaves

separatedbyameasurabledistance.Equipmenttodothisisavailablefromscientificsupplyvendors,suchasPASCO.

ThePoint

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Thespeedofawave,suchaslight,canbedeterminedfromitswavelengthandfrequency.Thewavelengthofamicrowave

ovencanbefoundbythedistancebetweenthenodesofaresonantstandingwave.

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Project85

Refraction.Howfastdoeslighttravelinairorwater?

TheIdea

Lighttravelsat itstopspeed inavacuumandat (nearly) itstopspeed inair.When lightmovesthroughothertransparent

materials,itslowsdown.Ifitgoesfromonematerialtoanotheratanangle,thelightwillbend.Themoreitslowsdown,the

moreitbends. Inthisprojectyouwillcomparehowmuchlightbendsinvariousmaterials.Thisbending iscalledrefraction

anditgivesusawaytodeterminehowfastlighttravelsinatransparentmaterial.

WhatYouNeed

squareorrectangularpieceofglassabout¼inchthickandafewinchesinlengthandwidth(atleasttwoopposing

sidesmustbeclear)

laserpointer

semicircularplasticcontainerfilledwithwater

protractor

Method

Laser

1.Placethepieceofglassonthepaper.

2.Tracetheshapeoftheglass.

3.Darkentheroom.

4.Putadotononesideoftheglasstoprovideatargetforthelaser.

5.Drawalineperpendiculartotheedgeoftheglassatthatpoint.Extendtheline,soitextendsundertheglass,aswell

asgoingintoit.

6.Placethelaser,soitsbeamformsananglewithrespecttotheperpendicularlineyoujustdrew.Markthepositionof

thelaser.

7.Darkentheroom.

8.Shine the laseranddirect itsbeamtoward the targetdot.Angle thebeamvertically, soyoucansee itspathboth

beforeenteringandafterexitingtheglass.(ItisOKifyoudon’tseetheentryandexitbeamsatthesametime.)

9.Placeadotwhereyouseethelaserbeamexitfromtheglassandoneortwodotsalongitspath.

10.Connectthedotwherethelightstrikestheglasswiththepointwherethelightrayemergesfromtheglassbackinto

theair.

11.Measuretheanglesthat:

–theincomingraymadewiththeperpendicularline(θi).–theraygoingthroughtheglassmadewiththeedgewherethelightenteredtheglass(θr).12.Trythiswithothertransparentmaterialssuchaswater(inaplasticcase).

ExpectedResults

Goingfromairintowater,thelightpathisbenttogiveasmalleranglewithrespecttotheperpendicularline.Specificresults

aregiveninthefollowingchart:

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WhyItWorks

TherelationshipbetweentheincidentandrefractedanglesisgivenbySnell’slaw,whichstates:

nisin(θi)=nrsin(θr)whereniistheindexofrefractionwheretherayisincidentandnristheindexofrefractionwheretherayisrefracted.Both

aremeasuresofthespeedoflightinthevariousmaterials,Theindexofrefractionforanymaterialisgivenbyn=c/v.The

physicalarrangementforthisisshowninFigure85-1.

Theindexofrefractionforair,whichis1.0,indicatesthatlightistravelingatitsmaximumspeed.

Becauselightslowsdowninglass,nforglassis1.45.

Figure85-1

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OtherThingstoTry

Findtheindexofrefractionfortheglassorwaterusingtheequation:

nisin(θi)=nrsin(θr)usingniforair=1.0andθIandθrasdefinedintheprevioussteptofindtheindexofrefractioninthematerialofinterest.Theindexofrefractionisgivenby:

n=c/v

Theindexofrefractionisameasureofthespeedoflightinaparticularmaterial,v,comparedtothespeedoflightina

vacuumwhichisgivenbyc=3.0×108m/s.Thespeedoflightinaparticularmediumisgivenbyv=c/nr.

ThePoint

Lighttravelsataslowervelocitywhenitgoesthroughmaterialsotherthanvacuumorair.Whenlighthitsaboundarygoing

fromamaterialwherethelightisfastertoonewhereitisslower,thelightbendstowardtheperpendicularline.

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Project86

Polarization.Sunglassesandcalculatordisplays.

TheIdea

Theorientationofthecrestsandtroughsoflightwavescanbehorizontal,vertical,oranythinginbetween.Unpolarizedlight

consistsofarandommixoforientations.Polarizedlighthasonlyonedirection.Thisgives it theuniquepropertiesused in

liquid crystal displays found inmany television screensandcomputermonitors. Sunglasses reduceglare byallowingonly

selectedorientationsofpolarizedlightthrough.Thisexperimentexploreshowtoidentifywhetherlightispolarizedandhow

thetransmissionofpolarizedlightcanbecontrolled.

WhatYouNeed

2polarizedsheets

calculatororotherLCDdisplay,suchasalaptopcomputer

polarizedsunglasses

lightsource

shallowtray

water

fewrocks

sheetofglass

optional:protractor,lightsensor

Method

Transmissionthroughpolarizedsheets

1. Takeoneofthepolarizedsheets.Holditinfrontofalightsource(alamporanopenwindow)androtateit.Turnthe

sheetafull360degrees,holdingthesheetsoitremainsroughlyperpendiculartoyourfieldofview.

2. Trythiswiththeothersheet.

3. Now,withbothsheets,holdtheminfrontofthelight,oneinfrontoftheother,androtateonlyoneofthem.Observe

whathappens.Addinothercombinations:rotatebothinthesamedirection,rotateboth,butindifferentdirections.

Describetheeffectofthesheets.Isthelightfromyourlightsourcepolarized?

4. Usinganondestructivemethod,suchasapplyingasmallpieceoftape,identifyanedgeoneach,whichwhenplaced

together,blocksthemaximumamountoflight.

5. Note:ThisisgoodtodousinganoverheadprojectororthelightfromanLCDprojector.

Reflections

1. Placeasmallflatmirrorfaceuponatable.

2. Placealightsourceononesideofthemirror.

3. View the reflected light throughoneof thepolarizedsheetsasyou rotate thesheet. Is that lightpolarized?View

througharangeofreflectedanglesfromnearlyperpendiculartoaveryglancingangletothemirror.

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4. Place the two sheets, one on top of the other, but with taped edges aligned, so both sheets have the same

polarizationplane.Whathappenswhenyourotatethesheets,bothwithrespecttothemirrorandtoeachother?

5. Repeat1–4,usinglightreflectedfromasquareofglass.

Laptop/sunglasses

1. HoldapolarizedsheetinfrontoftheLCD(liquidcrystaldisplay)ofalaptopcomputerordigitalcalculator.

2. Rotatethepolarizedsheet.WhatcanyouconcludeabouttheLCDofthelaptop?

3. Take the two lenses fromanold (no longerneeded)pairofpolarizedsunglasses.Hold them—one in frontof the

other—and view a light source. Are the glasses polarized? You also can try this with two pairs of polarized

sunglasses.

ExpectedResults

Lightwill pass throughpolarizedsheetswith little losswhen thedirectionsofpolarization forbothsheets lineup.As the

sheetsarerotated,moreandmoreofthelightisblocked.Withthedirectionofpolarizationofthetwosheetsatrightangles,

almostnolightcanpassthrough,asshowninFigure86-1.ThiscanbequantifiedinMalus’slaw,whichisaddressedlaterin

thissection.

Figure86-1

Figure86-2Percentageoflightblockedbypolarizingfilters.

Alightmeterisagoodwaytoquantifytheamountoflightpassingthroughafilter.Figure86-2providesanapproximate

visualreferencetoevaluatetheamountoflighttransmissionthroughasetofpolarizingfilters.

Reflected lightcanbepolarized.Thiscanbedeterminedbyobservingtheeffectofasinglepolarizedfilteronreflected

light.

ThelightfromaLCD,suchasalaptopscreen,isalsopolarized.Thiscanbeseenbyrotatingapolarizedfilter,suchas

polarizedsunglasses,infrontofanLCDscreen,asshowninFigure86-3andFigure86-4.

WhyItWorks

Lightisanelectromagneticwavethatpropagatesalongaline.Ifwecanimaginelookingdownthatline,wewouldseethe

wavesfrommostlightsourcesmovingupanddowninanydirection.Forunpolarizedlight,thewaveoscillationsarerandomly

distributed over 360 degrees. A polarized filter selects only one of the polarization planes. Reflection polarizes light by

favoringlightintheplaneofthereflectingsurface.

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Figure86-3Polarizedfilter(sunglasses)orientedtopasspolarizedlightfromlaptop.

OtherThingstoTry

Malus’slaw

Wesawhowthemorewerotatedthepolarizedsheets,thelesslighttheytransmitted.Here,wefindthephysicalmodelfor

thateffect.

1. Startwiththetwopolarizedsheetsoriented(withtapedsidesaligned)toallowthemaximumlighttobetransmitted.

2. Findawaytomeasureorestimatetheamountoflighttransmitted.Dependingonyourresources,thiscaninclude:

–Estimatingthetransmissionvisuallybyusingachartrangingfromwhite100percenttransmissiontoblack0percent

transmission.Figure86-5maybearoughguide.

–Comparingthetransmissionusingasetofcalibratedneutral-densityfilters(thatmaybeavailableinsomelabs).These

transmitaspecificamountoflightwithoutchangingthecolor,sotheymightserveasagoodvisualcomparison.

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Figure86-4Polarizedfilter(sunglasses)orientedtoblockpolarizedlightfromlaptop.

– Using a lightmeter tomeasure the light transmitted. The percent would be the ratio of the light transmitted at a

particularmisorientationangledividedby theamountof light transmitted through thepolarizedfilterswhen theyare

aligned.Thisworksbestiftheroomisdarkenedandthelightfromthesourceisisolatedfromthemeter.Onewayto

dothisistoputthelightinaboxandcutasquareholesmallerthanthefilters.Thelightmetercanbepurchasedfrom

asciencesupplycompanyormadefromasolarcellwithsolderwireleadsconnectedtoanammeter(asdescribedin

Project81).

3.Measureorestimatetheamountoflighttransmissionasafunctionofmisalignmentangleofthepolarizedsheets.Use

thefollowingdatatabletoorganizeyourdata.

TheexpectedresultsaredescribedbythisiscalledMalus’slaw.

Thegreaterthemisorientation,thelesslightistransmitted.Thedrop-off,however,isnotlinearbutis,instead,givenby:

Fractionoflighttransmitted,I/Io=cos2θ

TheexpectedresultsaregiveninFigure86-5.

FindBrewster’sangle

Previouslyinthissection,yousawthatlightreflectingfromapieceofglasscanbepolarizediftheangle(withrespecttothe

normal)isgreatenough.ThatangleiscalledBrewster’sangle.

1. Placeasheetofglassflatonatable.

2. Usingaprotractorasaguide, view the reflected lightatvariousangles.Useastraightedgepositionednear the

protractorasavisualguidetoestablishthereflectedangle.

3. Determine themaximum angle with respect to the perpendicular that results in reflected polarized light. That is

Brewster’sangle.

4. CompareyourresultwiththeexpectedvalueofBrewster’sanglegivenby:

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n=tanθpwherenistheindexofrefractionfortheglassandθpistheanglewherethereflectedlightiscompletelypolarized.

Figure86-5Malus’slaw.

Sometypicalvaluesaregiveninthefollowingtable:

Findinganobjectunderwater

1. Placeseveralobjects(coins,rocks)inapanofwater.

2. Covertheobjectswithseveralinchesofwater.

3. Establishalightsourceatanangle.

4. Findaposition toview thesurfaceof thewater,soyousee the reflected lightshimmeringat thesurfaceof the

waterobscuringtheobjectsbelow.

5. Viewthe lightusing thepolarizingfilter.Viewatanglesbothgreaterand lesser thanBrewster’sangle through the

polarizingfilter.Underwhatconditionsareyouabletoseetheunderwaterobjects?

ThePoint

Typical light sources, such as light bulbs or the sun, produce unpolarized light that has electromagnetic waves oriented

randomly.Lightcanbepolarizedbyfiltersorcertainreflectingsurfacesthatselectaspecificorientationofthelightwaves.

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Project87

Whatisthewireofafiber-opticnetwork?Totalinternalreflectionusingalaseranda

tankofwater.

TheIdea

Muchof thedigitalcommunicationthatcirculatesaroundtheworldonthe Internetconsistsof light travelingthousandsof

miles through glass threads thinner than human hair. Total internal reflection is the physical process that keeps these

informationpulsesconfinedwithinthesetinyopticalfibers. Inthisexperiment,youcansetupvariouswaystoexplorehow

transparentmaterialsguidelightbytotalinternalreflection.

WhatYouNeed

laserpointer

fishtank(preferablywithaglassbottom)

tablespoonofmilk

darkroom

sink

one2-Lclearplasticsodabottle

Method

Totalinternalreflectionfromthesurfaceofwater

1. Fillthetankwithwater.

2. Turnofftheroomlights.

3. Directthelaserfromthesideofthetankunderthelevelofthewatertowardthesurface.

4. Addenoughmilktothewaterinthetanksothepathofthelaserisvisibleasitpassesthroughthewater.

5. Ifthefishtankhasaglassbottom,directthelaserthroughthefishtankfromthebottomatvariousangles.

6. Determinethemaximumanglethatwillallowthelighttoemergefromthetank.

Aliquidlightpipe

1. Punchasmallholeabout1mmindiameterinthesideoftheplasticgalloncontainer.

2. Fillthecontainerwithwater.

3. Darkentheroom.

4. Asthewaterflowsfromtheholeintothesink,shinethelaserfromtheothersideofthebottle,butaimitatthehole.

5. Observehowthelightpassesthroughthebottleandisguidedthroughthewaterstreampouringoutofthebottle.

Thisisbecausethelightistrappedinthewaterstreambytotalinternalreflection.Withanindexofrefractionof1.33

forwater,any light incidenton thesurfaceatananglegreater than48.7degreeswillbe totally reflected.This is

muchlowerthantheanglesthelightmakeswiththewaterstream.

Acryliccylinderlightguide

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An acrylic (or other transparent material) makes a good demonstration of light trapped in a medium by total internal

reflection. Send the beam through one of the flat ends. Regardless ofwhat angle you direct the beam, the lightwill not

refractoutthroughthesidesofthecylinder.

Observinglightfibers

Opticalfibersshowveryconvincinglyhowlighttravelsthroughathintransparentmaterial.Opticalfibersareavailablefrom

scientificsupplycompaniesandnoveltylightingstores.

ExpectedResults

Lightpassingthroughthewaterandstrikingthesurfacepassesthroughtotheairiftheangleisabovethecriticalanglefor

water.

Figure87-1shows lightpassing throughplasticatanangle less than thecriticalangle.Notice thatmostof the light is

refracted(orgoesthrough)thelenswithasmallerpartofthelightbeingreflectedattheflatsurface.

However, once the incident angle coming from the plastic back into theair is greater than the critical angle for those

materials,thelightexperiencestotalinternalreflection,asshowninFigure87-2.Here,lightiseffectivelytrappedinsidethe

plasticandcannotemergebackintotheair.

Figure87-1Incidentlightisrefractedandreflected.

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Figure87-2Totalinternalreflectionofincidentlight.

WhyItWorks

When light enters a material where it goes faster, the angle approaches 90 degrees as the incident angle increases.

Becausetheangleofrefractioncannotbegreaterthan90degrees,lightabovethecriticalangleistotallyreflected.

OtherThingstoTry

Variable index of refraction. (Based on a lecture demonstration posted at the UCB web site:

www.mip.berkeley.edu/physics/E+60+40.html.)

Refraction takesplacewhen light goes fromonematerial to another. Fiber-optic cableandother optical devices take

advantageofavariableindexofrefractiontoguidethelightinachannel.Todothis:

1. Coverthebottomofanemptyfishtankevenlywithabout1cm(about½inch)ofgranularsugar.

2. Addwatertothetankasslowlyandcarefullyasyoucan,soyoudisturbthelayerofthesugaraslittleaspossible.

Warmwateratabout70degreesCwillenablethesugartodissolvemorequickly.

3. Fillthetankwithafewinchesorsoofwater.

4. Letthetankremainundisturbedforafewdays,allowingthesugartoslowlydissolve.Theconcentrationofthesugar

solution—and,asaresult,theindexofrefraction—willvarywiththeheightabovethebottomofthetank.

5. Darkentheroom.

6. Directa laserfromthesideof thetankatananglewithrespecttothebottomof thetank.Thebeamshouldbe

guided,asifthroughaninvisiblelightpipeinthetank.Thisuseofavariableindexofrefractionissimilartotheway

afiber-opticcableguidesalightbeam.Ifthelaserisdirectedatanangle,thelightmaygothroughseveralbounces

ifthetankislongenoughandthedistributionofthesugarisuniform.Thisalsoillustrateshowmiragesform.When

lightpassesthroughcoolerairtowarmerairoveraroadsurface,thevariableindexofrefractionguidesthelightina

waythatcreatestheillusionofwaterlyingontheroad.

Lightguides

Opticalfiberscanbefoundintoyandnoveltystores,andasapartofcertain lamps.Theseworkontheprincipleoftotal

internalreflectionandtheyshowhowlightcanbe“piped”aroundcorners.Asimilarwaytoexplorethisistoshinealaserinto

anacryliccylinder.Althoughagoodbitofscatteringiswithintheacrylic,thelightistrappedinsideinasimilarmannertoan

opticalfiber,asshowninFigure87-3.

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Figure87-3Lightcominginonesideofthetubeistrappedbytotalinternalreflectionandemergesfromtheotherside.

ThePoint

Iftheanglethatalightraystrikesasurfaceistoolarge,thelightwillnotpassthroughtotheothermedium.Thiscanonly

happenifthespeedoflightisfasterinthesecondmedium(oriftheindexofrefractioninthesecondmediumissmaller).For

anglesgreaterthanthatcriticalangle,nolightisrefracted,butisinsteadtotallyreflectedbackintothematerialfromwhichit

originated.

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Project88

Thedisappearingbeaker.

TheIdea

Thisdemonstrationletsyousetupacloakingshieldthatmakesaglassobjectdisappear.

WhatYouNeed

Pyrexbeaker

otherglassobjectssuchasPyrexstirringrodsandmagnifyingglasses

transparentcontainerlargeenoughtoholdthebeaker

cookingoil(suchasWesson,babyoil,Karosyrup,orlightandheavymineraloil)

Method

1. Placethebeakerinthelargercontainer.

2. Fillthecontainerwiththeoil.

3. Immersethebeakerintheoilandslowlypourtheoilintothebeaker.

4. Observewhathappenswhenotherglassobjectsareplacedintheoil(Figure88-1).

ExpectedResults

Astheoillevelrisesabovethebeaker,theglasscannolongerbeseen.Ifanymarkingsareonthesideofthebeaker,they

willstillbenoticeable,asseeninFigure88-2.

Ifyouuseotherliquids,similarresultsmaybeobtained,butyoumayhavetodosomefinetuning.Othertypesofglassand

other oils (including the “lite” version of cooking oils) may be less perfect, leaving some ghost images that are less

noticeable the fartherawayyour “audience” is.Amixtureofaheavyand lightmineraloil (ina ratioofabout2:1 tostart)

shouldmatchPyrexandbeadjustableforothertypesofglass.KarosyrupisaclosematchtoPyrexandcanbedilutedwith

watertomatchothertypesofglass.

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Figure88-1

Figure88-2Disappearingbeaker.

Themagnifyingglasswillnotenlargeimageswhensubmerged.

Thepreciseindexofrefractionforthesematerialsmayvaryslightlywithtemperature.Also,imperfectionsintheglassmay

makeitdifficulttomaketheverylasttracedisappearonsomesamples.

WhyItWorks

Objectsarevisibletotheextentthattheyareabletoreflectlight.Ifanobjectimmersedinaliquidhasanindexofrefraction

thatisdifferentthantheobject,someofthelightisrefractedthroughtheobjectandsomeisreflectedbacktotheobserver.

However, if the object has exactly the same index of refraction as the immersed object, the light will neither reflect nor

refractattheinterfacebetweentheobjectandtheliquiditisimmersedin.Inthatcase,theobjectwillappeartobeinvisible.

Lenses,suchasmagnifyingglasses,workbyvirtueoftheirindexofrefractionbeingdifferentthantheindexofthemedium

aroundit. Iftheindexofrefractionsurroundingthelensis increasedfrom1.0,whichistheindexofrefractionofair,toan

indexveryclosetoglass,thelightrayswillnotbebentthroughafocalpointandmagnificationwillnotoccur.

BothWesson cookingoil andPyrex glass havea nearly identical index of refraction of about n=1.474,making them

particularlywellmatchedforthisdemonstration.

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OtherThingstoTry

Asimilarexperimentalongtheselinesisfirsttopourawater-alcoholmixturetoabeaker,andthencoveritwithcookingoil.If

asmallenoughamountofalcoholisinthemixture(lessthantwiceasmuchoilaswater),theoilwillfloatanditwillalsonot

mixwiththealcohol-waterlayer.Ifyouaddafewdropsoffoodcoloringtothewater-alcoholmixture,theeffectiseasierto

see.Viewing from the top, thewater-alcohol layer is invisible.This is the resultof total internal reflectionat the interface

betweenthelayers.

ThePoint

Transparentobjectsarevisiblebecauseofreflectionfromtheirsurface.Transparentobjectswillpartiallyreflectandpartially

refractlightifthereisadifferencebetweentheirindexofrefractionandthatoftheirsurroundings.Iftheindexofthematerial

andtheirsurroundingsisthesame,theobjectwillappeartobeinvisible.

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Section8

HotandCold

Project89

HowmuchheatisneededtomeltGreenland?Heatoffusion.

TheIdea

Iceanywhererequiresacertainspecificamountofheattomelt.Icemeltsat0°C.Onceatthattemperature,theamountofheatneededdependsonlyonhowmuchiceyouhave.Heatcaneitherchangethetemperatureofsomethingorcauseitto

changefromonestatetoanother.Inthisexperiment,thatchangeisfromsolidtoliquid.Youwilldeterminehowmuchheatis

neededtomeltagivenmassoficebycarefullykeepingtrackoftemperaturechangesandheatflows.

WhatYouNeed

Styrofoamcup

cubeofice

graduatedcylinder(250mL)

water

thermometer

stirringrod

scale

Method

1. Fillthebeakerwithexactly150mLofwateratatemperatureofatleast25degreescentigrade.Thisresultsina

massofthewater,mw,of150g.

2. Removeanicecubefromthefreezerandletitsitoutuntilitjustbeginstomelt.Thisestablishesitstemperatureat

(verycloseto)0degreescentigrade.

3. Measurethemassoftheicecube,mice,ingrams.Ifsignificantmeltinghasoccurred,youcanuseapapertowelto

absorbanyexcessliquidwaterbeforemeasuringthemass.

4. Measuretheinitialtemperatureofthewater,Ti,beforetheicecubeisadded.

5. Dropintheicecube.Stirgently.Measurethefinaltemperature,Tf,assoonastheicecubehascompletelymelted.

6. Calculatehowmuchheatwasneededtomelttheicethroughthefollowingsteps(seeFigure89-1):

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Figure89-1Heatistransferredfromthewatertoraisethetemperatureoftheiceandwaterandtomelttheice.

–Heatextractedfromthewater

GivenbyQw=mwCw(Tf−Ti)whereCwisthespecificheatofwater=4.18J/g°C.Thismeansthat4.18joulesofenergy(whichishowenergyismeasured)areneededtoraiseeachgramofwaterevery1degreecentigrade.

–Heatneededtobringthemeltedicefrom0°CtothefinalliquidtemperatureGivenbyQmeltedice=miceCw(Tf−0)–Heatneededtomelt1gramofice

Hf=(Qw–Qmeltedice)/mice

ExpectedResults

TheexpectedresultisHf=334J/g.Thismeans334joulesofheatenergyareneededtomelt1gramofice.

WhyItWorks

Whenacubeoficeisplacedinabeakerofwater,someheatistakenfromthewater.Thislossofheatresultsinthewater

beingbrought toa lowerequilibriumtemperature,which is lower thanthestartingtemperature.Theheat lostby thewater

accomplishes two things:1) itmelts the ice,and2) itbrings the liquid resulting from themelting iceup to theequilibrium

temperature.Thisgivestheoverallequation:

Qw=Qmeltedice+miceHf

SolvingforHfgivestheequationusedtofindtheheatoffusionforice.

OtherThingstoTry

Determinethetemperatureofafreezer.Asbefore,placeanicecube(thistimeimmediatelyremovedfromthefreezer)ina

Styrofoamcupfilledwithwaterofaknowntemperature.Dothisbyusingtheknownvaluefortheheatoffusionoficeand

theheattransferequationusedpreviously.

Determinethetemperatureofahotobject(suchasared-hotnail)bymeasuringthetemperaturebeforeandtheequilibrium

temperatureafterimmersionoftheobject.Thensolvetheheatequationsfortheinitialtemperatureoftheobject.

CalculatetheamountofheatneededtomelttheGreenlandicecaps:Greenlandcontains2.85millioncubickilometersof

iceor1.4×1014icecubeseachwithamassof20g.Basedontheheatoffusionforice(0degreesC)determinedinthisexperiment,theGreenlandicecapswouldrequire9.5×1023Joulesofheatenergytomelt.

ThePoint

307

Whenobjectsatdifferenttemperaturesaremixed,theyresultinanequilibriumtemperaturethatisbetweenthehighestand

lowesttemperaturesinthemixture.Theamountofheatneededtocauseacertaintemperaturechangeforagivenmassof

materialischaracterizedbythespecificheatforthatmaterial.Inadditiontocausingtemperaturechangeinamaterial,some

heat(calledlatentheat)resultsinachangeofphasefromsolidtoliquid.

308

Project90

Awaterthermometer.

TheIdea

Allmaterials(withtheonenotableexceptionoficeataround4°C)expandwhenheated.Itishardtonoticethedifferenceinvolumebetweenahotcupofteaandthevolumeinthecupwhentheteacools.Thisexperimentgivesawaytointensifythe

effectofthethermalexpansion,soitcanbemeasuredandcomparedtoaknownvalue.

WhatYouNeed

250mLflask

2-holerubberstopperthatfitsintheflask

hotplate

1000mLbeaker(oronelargeenoughforyoutoplacetheflaskin)

glasstubethatfitsthroughtherubberstopper(about15incheslong)

water

glassthermometerthatfitsthroughthesecondholeofthestopper(ifyoudon’thaveathermometerthatworks,then

youneedaone-holestopper)

Vaseline(orglycerin)andatoweltohelpslidetheglassandthethermometerintothestopper

ruler

ringstandwithabeakerortesttubeclamp

Method

1.Determinetheradiusoftheglasstubeby:

–Partiallyfillingtheglasstubewithwater.

Placeyourfingeroverthetopofthetubetokeeptheliquidfromslidingoutwhileyouaremakingthismeasurement.

–Measuretheheight,ho,ofthewatercolumn.

–Releasethevolumeintothegraduatedcylinderandmeasurethevolume.

–ThevolumeoftheliquidmeasuredV=πhr2.–Theradiusofthetubeisr=(V/πho)½.2.Carefullyslidetheglasstubeintothestopper.UsealittleVaselineorglycerinasalubricantandprotectyourhands

withatowelasyoupush.Don’tforceit.Afewinchesofthetubeshouldextendbelowthestopperwiththereststicking

outabove.

3.Slidethethermometerintotheotherhole,sothebottomofthethermometerispositionednearthecenteroftheflask.

4.Completelyfilltheflaskwithwater.(Addfoodcoloringifyoulike—yourchoiceofcolor.)

5.Insertthestopper.Asmallamountofliquidmayspilloutoverthesideoftheflaskandsomemaybeforcedupthe

tube.

6.Placetheflaskwiththestopperinthebeaker.

7.Fillthebeakerwithwatertocovertheflask.

8.Placethebeakeronthehotplate.

9.Turnonthehotplate.TheapparatusforthisexperimentispicturedinFigure90-1.

10.Recordthetemperatureintheflaskandnotethepositionoftheliquidintheglasstube.(IfyouhaveaSharpiehandy,

markitontheglass.)

11.When the temperature in the flask risesa fewdegrees, record the temperatureandmeasure the increase in the

309

heightoftheliquidintheflask.

12.Theincreaseinvolumeforagiventemperature increaseisgivenbyV=πhr2,whereh isthemeasuredheight(inmeters)andristheinnerradiusoftheglasspreviously.Insettingthisup,someliquidlikelywillextendintothetube

atyourstartingtemperature.Ifthisisthecase,definethisasyourzeropointandtakehasthedistancethe liquid

rises intothetube. (Thesmalldifference in volume resulting from the liquid that initially rises into the tube isnot

significantforthismeasurement,butifyouareverypicky,youcancorrectforthisonprinciple.)

Figure90-1Waterthermometer.

ExpectedResults

Agivenvolumeofwaterexpandsbya factor that is0.000207 (or2.07×10−4)of itsoriginalvolumeforevery1degreeincreasecentigrade.Thisvolumeisdistributedbetweentheflaskandthetube.

WhyItWorks

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Nearly all materials expand when they are heated. The amount of expansion is characterized by something called the

coefficientofexpansion. Inthecaseofsolids, theexpansion inonedirection iscalledthecoefficientof linearexpansion.

Multiplyingtheoriginallengthbythecoefficientoflinearexpansiongiveshowmuchlongertheobjectis.

Volumeworksalmostthesameway,exceptinthethreedimensions.Thecoefficientofvolumeexpansion indicateshow

muchvolumeisaddedtoa(solidorliquid)materialforeverydegreethetemperatureincreases.

OtherThingstoTry

Design and calibrate a water thermometer using the coefficient of volume expansion for water and the dimensions you

determinedfortheglasstube.

ThePoint

Theamountamaterialexpandswhenheatediscalledthecoefficientofvolumeexpansion.Weconstrainedtheexpansionof

alargervolumeofwaterintheflasktoprimarilyonedimensioninthetube.Thismagnifiedtheeffectoftheexpansion,sowe

wereabletomeasureit.

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Project91

Whatisthecoldestpossibletemperature?Estimatingabsolutezero.

TheIdea

What is thecoldest thingpossible?Somepeoplemightsay it isgivingaphysics testonaFridayafternoonbeforewinter

break. (Now that’scold!)But, thecoldest temperaturepossible isabsolutezero.Thisexperiment isanice, simpleway to

estimatethisfundamentalpropertyofnature.Withsomeextracare,amoreaccuratevaluecanbeobtained.Weknowthat

mattercontractsasitgetscold.Thebasicideahereistodeterminewhatwouldbethetemperatureifthevolumewereto

contracttothepointwhereitapproachedzero.Wecan’tgettothatpoint.Infact,wecan’tevengetcloseinanordinarylab.

But,wecanmeasurehowmuchthevolumechangesforagivenchangeintemperatureandmakeagraphtodetermineat

whattemperaturethevolumewouldbezero.Thattemperatureisabsolutezero.

WhatYouNeed

Toestimateabsolutezero

250mLPyrexflask

pairoftongssuitableforsafelyhandlingahotflask

beaker(largeenoughtofullyimmersetheflask)

hotplate

thermometer

bucket

graduatedcylinder

Tomeasureabsolutezerowithgreaterprecision

Atemperaturevolumeorpressure-volumeapparatus,suchasshowninFigure91-1.

Method

1.Putthebeakeronthehotplate.

2.Fillthebeakerwithwatertoalevelthatwillallowtheflasktobeimmersedwithoutcausingthewatertooverflow.

3.Turnonthehotplate.

4.Placetheemptyflask inthebeaker,so it isheatedfromoutside,butwithouthavingtheheatedwaterspill intothe

flask.

5. After the air in the flask has had a chance to reach equilibriumwith the heatedwater (about 5–10minutes at a

constanttemperature),measurethetemperatureofthewater.Theboilingpointisagoodstablemeasurementpoint,

butatemperaturelessthanthiscanbeusedifitisstable.

6.Fillthebucketwithcoldwater.Youcanuseicetobringthetemperaturedown.

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Figure91-1CourtesyPASCO.

7.Removetheflaskandimmediatelyplaceitnecksidedowninthebucket.Holdtheneckoftheflaskunderwaterasit

cools.Youmayfindithelpfultolightlyinsertarubberstopperwhileyouaretransferringtheflask.Youcanalsotryto

useaone-holestoppertemporarilypluggedwithashortsectionofastirringrod.

8.Once(inyourjudgment)itreachesequilibrium,measurethetemperatureofthewaterinthebucket.Thisshouldtake

lessthanoneminute.

9.Theairhascontractedandsomewaterhasentered the flask.Measure thevolumeof thewater in the flask. (The

mostaccuratereadingoccurswhentheairpressureaboutthewaterisinequilibriumwiththeoutsideair.Thiscanbe

establishedbyraisingthebottomoftheflasksothatthe liquid level intheflask isatthesameheightasthe liquid

levelinthebucket.)SeeFigure91-2.

10.Subtractthevolumeofwaterfromthetotalcapacityoftheflask.

11.Plotthetwopointsyoumeasuredonagraphwithvolumeonthey-axisandtemperatureonthex-axis.Leaveenough

roomonbothaxessothatthepointwherethe lineconnectingthepointsextrapolatestozerovolumefitson the

graph.Drawthatlineanddeterminethetemperaturewherethevolumewouldbezero.

Figure91-2WhenthetemperaturecoolsfromT1toT2thevolumechangesfromV1toV2.

ExpectedResults

Theacceptedvalueforabsolutezerois0Kor−273°Cor−459.7°F.However,becausethefirstpartofthisexperimentisaballparkmeasurement,valuesanywherefrom−175to−350°Carereasonableextrapolations.Althoughthisisawiderange,theconceptthatextrapolatingthevolumeversustemperaturecurveuntilthevolumegoestozeroissignificant.Statistically,

weknowweareonveryshakygroundbecausewearegeneratingdatapointsthatarefarremovedfromthetemperaturewe

areextrapolatingto.

WhyItWorks

Charles’slawstatesthatT1/V1=T2/V2.Thiscanbeinterpretedassayingthatthevolumeofagasisdirectlyproportionalto

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thetemperature.Thelowesttemperatureconceivableisthetemperaturewhenthegascontractstoazerovolume.Thiscan

never actually occur. If we extrapolate the linear relationship between temperature and volume to zero volume, you can

determineavalueforabsolutezero.

Similarly,Gay-Lussac’s lawstatesthatT1/P1=T2/P2.Absolutezero isthetemperaturewherethetemperaturepressure

lineisextrapolatedtozeropressure.

OtherThingstoTry

The accuracy of this measurement can be improved on by using the Gay-Lussac’s apparatus and extrapolating the

temperatureversuspressurecurvetozeropressure,asshowninFigure91-3.

TwodifferentsetsofmeasurementsoftemperatureversuspressureareshowninFigure91-4.

Thepointwherethepressureextrapolatestozeroisinterpretedasabsolutezero,asshowninFigure91-5.

Figure91-3TheGay-Lussacapparatusisusedtomeasuretherelationshipbetweenpressureandtemperature.

Onesourceoferrorindeterminingthechangeinvolumewithtemperatureisthepresenseofwatervaporintheflask.Use

ofoil insteadofwater to immerse theflask inavoids thisproblem.This isamessierbutmoreaccurateway toestimate

absolutezero.

Absolutezerocanbedeterminedbymeasuringthespeedofsoundatdifferenttemperatures,asdescribedin“Determining

AbsoluteZeroUsingaTuningFork,”byJeffreyD.Goldader(ThePhysicsTeacher46,April2008,206–209).

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Figure91-4Measurementoftemperatureversuspressure.

Figure91-5Extrapolationoftemperatureversuspressuredatatozeropressuretofindabsolutezero.CourtesyPASCO.

ThePoint

Absolute zero cannot be measured directly. It can be determined by extrapolating measurements of pressure versus

temperaturetozeropressure.Similarly,absolutezerocanbedeterminedbyextrapolatingmeasurementsofvolumeversus

temperaturetozerovolume.

315

Project92

Liquidnitrogen.

TheIdea

Theairwebreath isabout78%nitrogen.Typically this isagasbutwhenbroughtdowntoanextremelycoldtemperature

nitrogenbecomesaliquid.Notonlyisliquidnitrogenfuntoplaywith,butitgivesyouanopportunitytobegintoexplorelow-

temperaturephysics.

WhatYouNeed

safetygoggles

tongsandthermalmitt

dewar(specificallydesignedtocontainliquidnitrogen)

sampleofliquidnitrogeninasecurecontainer

plasticbeaker

tableorothersurfacethatwillnotbeharmedbyverycoldtemperatures

Pyrexbowllargeenoughtoholdasmallquantityofliquidnitrogenandimmersetheotherobjectslistedhere

12inches(approximately)ofleadtinorothersolderwire

20ghookedmass

flowers

banana

hammer

metaltubewithoneendopenandtheothersealed

medicinebottlewitheasysnapon/snapofflidora35mmfilmcanister

corkthatlooselyfitsintotheopenendofthemetaltube

balloon

Method

Safety

1. Liquid nitrogenmust be handled safely. Thismeans itmust be stored in a specially designed container called a

dewar,whichisintendedforthispurpose.Donotputliquidnitrogeninatypicallunchboxthermos,whichshouldnever

beusedforliquidnitrogen.

2. Liquidnitrogenissocold,itcanfreezehumanskininaveryshorttime.Foralltheseactivities,allparticipantsshould

wear safety goggles and avoid any sustained contact with skin. Be especially carefully to avoid splashing liquid

nitrogen, which could get trapped under clothing and cause freezing. Also, remember, objects that have been

immersed in liquid nitrogen have themselves been brought to a very low temperature and should be handled

appropriately.

Splittingabanana

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1. CarefullypoursomeliquidnitrogenintothePyrexbowl.

2. Using the tongs and thermal mitt, immerse the banana into the liquid nitrogen for about 15–30 seconds. Initial

bubblingandvaporizationdiminishasthebananaapproachesequilibriumwiththeliquidnitrogen,asshowninFigure

92-1.

Figure92-1Freezingabananainliquidnitrogen.CourtesyPASCO.

3. Removethebananaandplaceitonthetable.

4. Take the hammer and strike the banana, as shown in Figures 92-2 and 92-3. (For contrast, you can strike an

unchilledbananaeitherbeforeorafter,showingtheeffectofthemuch-more-brittlefrozenversion.)

Frozenflowers

1. Usingthesamebowlasthepreviousexperiment,immersesomefreshflowersintheliquidnitrogen.

2. Dropthebouquetonthefloororstrikethemonthetable.

Figure92-2Strikingadeep-frozenbananawithahammer.CourtesyPASCO.

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Figure92-3Normallysoftandpliableobjectswhendeepfrozenbecomebrittle.CourtesyPASCO.

Solderspring

1. Formthepieceofsolderintoacoilroughly¾inch(1–2centimeters)indiameter.

2. Noticethelackofstiffnessinthespring.

3. Immersethespringintheliquidnitrogenforroughly15–30seconds.

4. Hang a 20 g (or so) hooked mass from the frozen spring and compare its stiffness with that of the room-

temperatureversion.

Balloon—filledwithair

1. Blowuptheballoonandtieaknotintheopenend.

2. Immersetheballoonintheliquidnitrogen.

3. Observewhathappensastheballooniscooled.

4. Removetheballoonfromtheliquidnitrogenandagainobservewhathappens.

Balloon—filledwithliquidnitrogen

1. Pourasmallamount(startwithabout10mL)ofliquidnitrogeninaballoon.

2. Tieaknotintheopenend.

3. Settheballoononatable.

4. Stepbackandmakesurenooneisnearthe(expanding)balloonandespeciallymakesurenoone’sfaceiscloseto

theballoon.

5. Observewhathappensastheballoonisexposedtothewarmerairtemperature.

Prescriptioncontainer/Filmcanister

1. Placethefilmcanister(oraplasticprescriptioncontainerwithasnap-offlid)onatabletoporonthefloor.Donot

useaprescriptioncontainerwithascrew-onorachild-prooflidthatdoesnoteasilysnapoffwithmoderateforce.

2. Poursomeoftheliquidnitrogenintotheplasticbeaker.

3. Poursomeoftheliquidnitrogenfromtheplasticbeakerintothefilmcanister.Fillthefilmcanisterabout¼fullwith

liquidnitrogen.

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4. Snaponthetop.

5. Standbackaspressurebuildsupinthecontainer.

Corkgun

1. Placethecorkgunwhereitisaiminginasafedirection(andspecificallynotdirectedtowardanyone’sface).

2. Pourabout50mLofliquidnitrogenintothecylinder.

3. Lightlyplacethecorkintheopenendofthecylinder.Donotjamthecorkinsotightlythatitcannotbepushedout

bythepressurethatwillbuildupinthecylinder.

4. Standback.Pressurewillbuildupastheliquidnitrogenevaporates.

ExpectedResults

Thefrozenbananaandflowerswillshatter.Thesolderwilltemporarilybecomemuchmorespring-like.Theair-filledballoon

will shrink as the air inside contracts from the extreme cold, and then it will re-inflate as it warms up again. The liquid

nitrogen-filledballoonwillexpandandpossiblyburst.Thelidsofthefilmcanister/prescriptionbottlewillpopoff.Thecorkwill

shootoutofthemetalcylinder.

WhyItWorks

Objectsbecomemorebrittleandcontractfromtheextremecold.Astheliquidnitrogenevaporates,itoccupiesamuchlarger

volume.Foragivenvolume,thegashasamuchlargerpressure.

OtherThingstoTry

For many experimenters, liquid nitrogen may not be easily available on a daily basis. While you have a supply of liquid

nitrogenavailable,youmaywanttoconsiderdoingtheotherprojectsthatalsorequireliquidnitrogen,suchasProject101

(effectoftemperatureonresistance)andProject106(superconductivity).

ThePoint

Liquidnitrogenprovidesanopportunitytoexplorelow-temperaturephysics.This includesmakingnormallyelasticmaterials

brittle.Materialscooledbyliquidnitrogencontract.Asliquidnitrogenevaporates,itexpands.

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Project93

Boilingwaterinapapercup.

TheIdea

Isitpossibletoboilwateroveraflameinapapercup?Thisprojectletsyoufindoutwhythisispossible.

WhatYouNeed

2 paper cups—most “paper” cups have a thin coating ofwax, which can still be used, but if you can get them,

uncoatedcupsarepreferable

water

flame—amatchoraBunsenburner

thermometerordigitaltemperaturesensor

Styrofoamcup

sand(enoughtopartiallyfillapapercup)

waterballoon

paperbag

Method

1. Fillthepapercupnearlytothetopwithwater.

2. Holdthecupovertheflame.

3. Continuedoingthisuntileitherthepaperburnsorthewaterboils.Optional:measurethetemperatureasitisheating

up.

4. Fillthesecondpapercupwithsand.

5. Holdthiscupovertheflameandobservetheeffectoftheflameonthecup.

6. FilltheStyrofoamcupnearlytothetopwithwater.

7. Holdthiscupoftheflameandobservetheeffectoftheflameonthecup,asshowninFigure93-1.

ExpectedResults

Thewaterwillboilinthepapercup.Ifthecupiscoatedwithwax,thewaxmaymelt,especiallyabovethewaterline.Ifthere

isacircularrimonthebottom, itmayburnwithoutburningthroughthecup.Thepapercupfilledwithsandwillchar,but it

won’tnecessarilyburstintoflames.TheStyrofoamwillmeltand,wheretheflameisapplied,possiblyleaveaholeintheside

ofthecup.

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Figure93-1Boilingwaterinapapercup.

WhyItWorks

When heat is added to water, its temperature increases until it reaches the boiling point of water at 100°C. The paperdoesn’tburnbecauseheatisconductedawayfromthepaperbeforeitcanreachitskindlingpoint(thetemperaturewhereit

beginstoburn).Paperbeginstoburnataround233°C(whichisclosetothenominalvalue451°Fforpaper,madefamousinRay Bradbury’s novel Fahrenheit 451). The water temperature can increase until it boils and still remain well below the

kindlingtemperatureofpaper.

Sandconductsheatawayfromthepaper.However,unlikethepaper,sanddoesnotundergoaphasechangesaswater

doesatitsboilingpoint.Thetemperatureincreasesabove100°C.Thisiswhyweseecharringinthepapercupcontainingsand.

TheStyrofoamisaninsulator.Asaresult,thewaterdoesnotconductheatawayfromtheStyrofoamcupasitdoeswith

thepapercup,whichconductsheatmuchmorereadily.ThisexplainswhytheflamemeltstheStyrofoam.

OtherThingstoTry

Analternativeapproach is towrapapieceof paperaroundametal pipeand note its response toa flame. Ina similar

manner,themetalpipeconductsheatawayfromthepaperbeforeitcanstarttoburn.

Fillthepaperbagwithwaterandholditovertheflame.Thewaterconductsheatawayfromthepaperatafastenough

ratetokeepitfromburning.

ThePoint

Phasechangesinmatter,suchasthetransitionfromliquidtovapor,takeplaceataconstanttemperaturecalledtheboiling

point.Aliquidcannotexceedtheboilingpointuntilalltheliquidhasevaporated.Materialssuchassandconductheatmuch

betterthanair.SomematerialssuchasStyrofoamaremuchbetterinsulatorsthanothermaterials,suchaspaper.

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Project94

Boilingwaterwithice.

TheIdea

Inthisproject,youuseapieceoficetocauseacontainerofverywarmwatertostartboiling.Thisisdefinitelynotwhatmost

peoplewouldexpect.

WhatYouNeed

PyrexErlenmeyerflask(oraFlorenceflaskwithapartiallyflatbottom)

rubberstopper(withoutholes)

beakertongs(orovenmitt)

water

fewicecubes

hotplate

ringstandwitharingsmallenoughtosupporttheflaskupsidedown

optional:belljarandvacuumpump,beaker

Method

1. Partiallyfill theflaskwithwater.Thereshouldbeagapofan inchortwoabovethewater levelwhenit isupside

down.

2. Placetheflaskonthehotplate,asshowninFigure94-1.

3. Keeptheflaskonthehotplateuntilthewaterboils.

4. Removetheflaskfromthehotplate.

5. Withoutdelay,puttherubberstopper(snuggly)intheflask,carefullyturnitupsidedown,andplaceitinthering.Use

anovenmittortongstohandletheflask.

6. Thewater(havingcooledslightly)shouldnowbestillquitehot,butnolongerboiling.

7. Positionafewicecubesontheflatoftheflaskandobserve.

ExpectedResults

Shortlyaftertheicecubesareplacedonthebottomoftheflask,bubblesstarttoemergefromthetop(nearthestopper).

These bubbles continue and the water in the flask boils for a short time. Careful observation should convince anyone

watchingthatthebubblesarecomingfromtheliquiditselfandarenotaleakintherubberstopper.SeeFigure94-2.

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Figure94-1Bringingaflaskfilledwithwaterto(justunder)boling.

WhyItWorks

When a vapor (such as the air/water vapor mixture) is cooled, it contracts. As the volume of gas above the hot water

decreases, thepressurealsodecreases.Waterboilsat100°C(212°F)atstandardatmosphericpressure,butataslightlylowertemperaturewhenthepressureabovetheliquidisreduced.

Figure94-2Boilingwaterwithice.

OtherThingstoTry

Youcantrythisanotherway:

1. Fillabeakerwithwater.

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2. Placeitonahotplateandbringittoaboil.

3. Removethebeakerfromthehotplateandletitcooluntiltheboilingjuststops.

4. Placethebeakerinavacuumchamber(belljaronavacuumplate).

5. Attachandturnonthevacuumpumptoevacuatethechamber.

6. Comparetheeffectofdirectlyapplyingavacuumtothereducedpressurecausedbytheice.

ThePoint

Waterboilsatalowertemperaturewhenthepressureoftheairaboveitislowered.

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Project95

Seebeckeffect/Peltiereffect.Semiconductorheating.

TheIdea

Muchofphysicsconcernsitselfwithhowoneformofenergyischangedintoanother.Thisexperimentexploreshowheatcan

causeanelectricalcurrenttoflow.Althoughthisisnotyetefficientenoughtobeusedasasignificantsourceofelectrical

power,itiswidelyusedintheformofthermocouplestomeasuretemperature.ThisisknownastheSeebeckeffect.

Thereverse—whereelectricalcurrentflowingthroughcertainmaterialsresultsinonepartofthecircuitgettinghotandthe

other part getting cold—is known as the Peltier effect. Unwanted heat is dissipated by electronic components. These

componentsmustbecooledtofunctioncorrectly.Peltiercoolershavenomovingpartsandhavebeenusedtocoolhigh-

speedcomputermicroprocessors.Theyarealsousedinsteadofdryiceincloudchambers.(SeeProject125.)

WhatYouNeed

voltmeter(ormultimeterconfiguredasanvoltmeter)

ammeter(ormultimeterconfiguredasanammeter)

variableDCpowersupply

jumperswithalligatorclips

1000ohmresistor

24-inchlengthsofvarioustypesof(uninsulated)metalwire,includingiron,copper,constantan,andaluminum

heatsource,suchasacandle,Bunsenburner,orasolderingiron

icecubes

optional:2thermocouplestobeusedastemperaturesensors

Method

Seebeckeffect

1. Selecttwodifferentwirematerials.Taketwopiecesofthefirstmaterialandonepieceofthesecondmaterial.Let’s

saywestartwithtwopiecesofironandonepieceofcopper.

2. Attacheachendofthecopperwiretoeachofthetwopiecesofironwirebytwistingaboutaone-halfinchlengthof

thewiretogether.

3. Connectthetwounattachedendsoftheironwiretothepositiveandnegativeterminalsofthevoltmeter.SeeFigure

95-1.Setthevoltmeteronthemostsensitivesetting.The250mV(0.250V)rangeisagoodplacetostart.

4. Measurethevoltageatroomtemperature.(Momentarilydisconnectoneofthevoltmeterconnectionstoverifythat

thevoltageyouarereadingistheresultofthecircuityousetup,ratherthanasmallstrayvoltagereading.)

5. Touchonejunction(twistedwireconnection)totheice,leavingthesecondjunctionatroomtemperature.Howdoes

thataffectthevoltagereading?

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Figure95-1WiringarrangementformeasuringtheSeebeckeffect.

6. Placethesecond junction in theheatsourceandseewhathappens.Becarefulbecausethevariousmetalwires

conductheatandcanburnanythingthatcomesincontactwithit.

7. Trythiswithasmanymaterialcombinationsasyoucan.

8. Placeatemperaturesensoroneachofthetwistedmetaljunctions.Varythejunctiontemperatures.Plotthevoltage

asafunctionofthedifferencebetweenthetwojunctiontemperatures.

Peltiereffect

1. Asbefore,connecteachendofonepieceofwiretoapieceofasecondtypeofmetalwire.

2. Connect the components as a series circuit consisting of thewires, the ammeter, a 1000 ohm resistor, and an

ammeter.ThiscircuitisshowninFigure95-2.

3. AdjusttheDCpowersupply,soabout10mA(10milliampsor0.01amps)isflowingthroughthecircuit.(Youcanuse

a9-voltbattery insteadofanadjustableDCpowersupply,which results inslightly less than thiscurrentwith the

1000ohmresistor.)

4. Putwateroneachofthejunctions.Whathappens?Reversethedirectionofthecurrentflowbyexchangingthewire

connectedtotheDCpowersupply.Howdoesthataffectwhatyoufind?

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Figure95-2ApparatusforthePeltiereffect.

5. Monitor the temperature of each of the junctions as you vary the current flowing through the circuit. Plot the

temperaturesofeachjunctionandthedifferenceversusthecurrent.

ExpectedResults

IntheSeebeckeffect,atemperaturedifferenceatthetwojunctionsresultsinavoltagegeneratedthroughthecircuit.

ThePeltiereffectresultsintemperaturedifferencesatthejunctionswhenacurrentflowsthroughthecircuit.

WhyItWorks

A temperature difference between two dissimilarmetals results in an electrical potential that drives a current through a

circuit.Thereverseeffectcausesatemperaturedifferencewhenacurrentflows.

OtherThingstoTry

Commercial thermocouples that employ dissimilarmetals are based on the Peltier effect and can be used to study this

principle. Some temperature control devices that serve as a means of studying the Seebeck effect are available

commercially.

ThePoint

The Seebeck effect and Peltier effect describe a set of interactions between the thermal properties and the electrical

propertiesofmatter.

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Section9

ElectricityandMagnetism

Project96

Staticcharges.

TheIdea

AccordingtoNewton’slawofuniversalgravitation,anymassexertsaforceonanyothermass.Electricchargesworkina

verysimilarway.Thefartherawayyouget,theweakertheforce.Becausetheelectricforceissomuchstrongerthanthe

gravitational force, it is much easier to measure. This experiment explores the nature of the electrostatic force and

establishesthebasisforCoulomb’slaw.

WhatYouNeed

2pithballsorconductivelycoatedStyrofoamballs(conductivelycoatedping-pongballsarealsoanoption)

2piecesofstringabout16inchesinlength

movableringstandwithapendulumclamp(orotherhorizontalsupport)

smallnonconductivepostonastand(thepostshouldbeafewinchesinlengthandconsistofathinwoodendowel

orashortglassorplasticrod)

ruler

rubberrod/woolpair(orequivalent)toapplyachargetothepithballs

optional:lightsourcetoprojecttheimageofthepithballsontoascreen(anoverheadprojectorLCDprojectorcan

servethispurpose)

Method

1. Attachonesideofeachofthetwostringstothepithball.

2. Attachtheothersidesofthestringtothependulumclampseparatedbyafewinches,sothepithballcanswingin

onlyonedirection,asshowninFigure96-1.

3. Attachtheotherpithballtothenonconductivestand.

4. Theswingingpithballshouldbepositionedsoitcanonlyswingclosertoandfurtherfromthestationaryball.

5. Drawareferencemarkonthebottomoftheringstandtoindicatetherestpositionoftheswingingpithballwithout

beingsubjectedtoanyforceotherthangravity.

6. Vigorouslyrubthewoolagainsttherubberrodtochargeitup.Toucheachofthepithballstoapplythesamecharge

tothem.Touchingthetwoballstogetherwillmakethechargesnearlyequal,butitisnotnecessarytodothis.

7. Startwithadistancebetweenthepithballsthatallowstheswingingballtohangvertically.

8. Slowlybringtheswingingpithballcloseruntiltherepulsionbetweenthetwopithballscausestheswingingpithball

tomoveawayfromthestationaryball.

9. Measurehowfartheswingingpithballmoveshorizontally.Youmaydothisbyobservingfromaboveandmeasuring

thedistancetheballhasmovedfromthereferencepoint.

10. Recordthehorizontaldistancebetweenthecentersofeachofthepithballs.

11. Repeatthismeasurementafewtimesbymovingtheswingingpithballinalittlecloser.

12. Thehorizontalseparation,x,betweentheunconstrainedpithballanditsequilibriumpositionisagoodindicationof

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theforce.(Thiscanactuallybeworkedoutintermsoftheforce,butthisisunnecessarytoexplorethekeypointof

this experiment.) For small angles that the pith ball makes with the vertical, the electrostatic force is directly

proportionaltotheseparationfromequilibrium.

13. Theseparationbetweenthestationaryballandtheequilibriumpositionsisdesignatedasd,asshowninFigure96-2.

Thetotaldistancebetweenthetwopithballsisgivenbyd+x.Makeagraphoftheseparationfromequilibrium,x,

andthedistance,d+x,betweentheballs.

Figure96-1Twounchargedballsinequilibriumposition.

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Figure96-2Twochargedballsshowdisplacementfromequilibriumposition.

ExpectedResults

Thecloserthetwoballsget,thegreatertheforce.

Thisrelationshipisnotlinear.

Theclosertheballsget,thefastertheincreaseinforcebetweentheballs.

Specifically,thisisaninversesquarerelationship.

Overall,thisexperimentworksbestonadaywithlowhumidity.

WhyItWorks

Coulomb’s law states that the force (in newtons) between two charges, q1 and q2 (in Coulombs or C), separated by a

distance,d(inmeters),isgivenby:

wherekistheCoulombconstant=9.0×109m2/C2.

OtherThingstoTry

Findinghowmanyelectronsareonachargedballoon.

Hangtwoballoonsafterfirstdeterminingtheirmass.Chargethemandtouchthemtogether,sotheyhaveroughlythesame

charge.TheCoulombforceresultsintheballoonsrepellingandseparating,asshowninFigure96-3.

Thenumber,n,ofelectronsoneachoftheballoonscanthenbedeterminedfrom:

whereqisthechargeon1electron

=1.6×10−19CkisCoulomb’sconstant=9.0×109m2/C2

misthemassofeachballoon

andθistheanglethestringofeachballoonmakeswithaverticalline.

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Figure96-3Twoballoonswithlikechargesrepel.

TheCoulombforcecanalsobeexploredinthefollowingsimpledemonstrations:

Chasingacan

Achargedrubberrod,suchastheonepreviouslyusedtochargethepithballs,inducesacurrentinacan.Thisenablesyou

torollthecanbackandforthacrossthetable,asiftherodwereamagicwand.

Bendingwater

Athinstreamofwaterfromafacetcanbebentbyachargedrod.

Tape

Thesimplestofallistotakesometransparenttapeandadhereittoatable.Afterpullingitup,thetapewillhaveacquireda

chargethatwillbeattractedorrepelledbyothernearbyobjects.Twosimilarpiecesoftapeacquiresimilarchargesandare,

therefore,repelled.

Plasmaglobe/Sunderball

Thisisatrue“evilgenius”propthatlookslikesomethingoutofaFrankensteinmovie.Asmallteslacoilproducesa large

voltagedifferenceinsideaglassbulb.Thisissimilartothewaythatchargebuildsupinclouds.Minilightningboltsdischarge

throughaninertgasinthebulb,producinganeerieglow.Theelectronsinthegasflowtotheelectricalgroundharmlessly

providedbyafingertouchingtheouteredgeoftheglassasifthepersontouchingtheoutsideoftheglobewasahuman

lightningrod.Thisissafetodobecausethecurrent(amps)flowingisverysmall.SeeFigure96-4.

FurtherAnalysis

ApplyanExcelcurvefitforthegraphoftheseparationfromequilibrium,x,versustheseparation(d+x)betweentheballs.A

scatterplotwiththepoweroptionselectedshouldindicatethebestfitclosestto–2,whichisaninversesquarerelationship.

Youcouldalsoplotxversus1/(d+x)2.Alinearfittothisgraphwouldindicateaninversesquarerelationshipbetweenx

331

(whichisanindicatorofthemagnitudeoftheforce)andd.

Figure96-4Plasmaglobe.

ThePoint

The force between two charges is directly proportional to the product of the charges and inversely proportional to the

distanceseparatingthechargesasgivenbyCoulomb’slaw.

332

Project97

Makinglightning.ThevandeGraaffgenerator.

TheIdea

AvandeGraaffgeneratorbuildsupstaticelectriccharges,whichwhendischarged,producevisiblelightning-likesparks.This

isoneofthemorememorablephysicsexperimentsandprovidesagreatintroductiontothebasicideasofelectricity.

WhatYouNeed

vandeGraaffgenerator

groundingsphere

groundingwire—withalligatorclipterminationsorjustplaininsulatedwirewiththeendsstripped

confetti,paperholesfromaholepuncher,RiceKrispies

stripsofpaper

scotchtape

afewaluminumpiepans(thesmallonesthatareabout4inchesindiameterarepreferable)

electroscope

glassrodandsilk,rubberrod,andwoolorfur

short(12inchorso)neonlightbulb

insulated(plastic)crate

othervandeGraafftoys:spinner,sparkgap

electroscope

Method

Awordaboutsafety

When used as intended and according to manufacturer’s specifications, this is a safe experiment. The van de Graaff

generator produceshigh voltages.Thesecanbeover20,000 volts,whichmay soundhigh.However, similar voltagesare

producedbyscrapingyourshoesacrossacarpetonadayoflowrelativehumidity.Thevoltageishigh,butthecurrentisvery

low,sothehighvoltageisnothazardousbecauseveryfewelectronsareinvolved.

Removeall electrical devices from your pockets orwrist. Set up a safe areawith unobstructed access to the van de

Graaffgenerator.

Herearesomeconsiderations:

Sparkscandamageelectronicdevices,includingcellphones,audiodevices,calculators,computers,digitalwatches,

andpacemakers.

Thisactivityisfunbecauseofthedramaticandsuddenstaticelectricdischarges.However,makesurenooneisput

atriskbyanyone’ssuddenreactionstothisapparatus.

Becarefulnottobuilduphigher-than-intendedchargesusinglonghumanchainsorotherstoragedevices,suchas

capacitorsorLeydenjars.

Makesuresparksarenotnearflammablematerials,suchasnaturalgaspipesorcombustiblelaboratorychemicals.

Lightning

333

1. PlacethevandeGraaffgeneratoronatableandplugintheelectricalchord.

2. PositionagroundingelectrodeafewcentimetersfromtheconductingsphereofthevandeGraaffgenerator.Ifyou

don’t havea discharge sphere purchased for this purpose, you can improvise using ametal rod, such as a ring

stand.

3. Attachawirebetweenthegroundingelectrodeandanelectricalground,suchasawaterpipeorametalbeamthat

ispartofthebuildingstructure.

4. TurnonthevandeGraaffgenerator.

5. Darkentheroom.

6. Move the conducting sphere of the van deGraaff generator back and forth, and observewhat is themaximum

distanceadischargewillcross.

7. Placeasheetofpaperinthepathofthespark.Doesasheetofpaperstopthespark?

8. TurnoffthegeneratorandtouchthegroundingspheretotheconductingsphereofthevandeGraaffgeneratorto

removeanyresidualcharge.

Paperstrips

1. Groundtheconductingsphere.

2. UsetapetoattachstripsofpapertothetopoftheconductingsphereofthevandeGraaffgenerator.

3. Turnonthegeneratorandobservethepaperhairsseparatingandstandingonend,asshowninFigure97-1.

4. Turnthegeneratoroffandgroundtheconductingspherewiththegroundelectrodetoremoveanyresidualcharge.

Ahair-raisingexperience

1. Groundtheconductingsphere.

2. PlaceaninsulatingsurfaceonthefloornearthevandeGraaffgenerator.Aninvertedplasticcrateworkswellfor

thispurpose.Thereasonfordoing this is tomakesurenodischargeoccurs toconductors,suchaswaterpipes,

underthefloor.

Figure97-1Likechargesrepel,causingthepiecesofpapertoseparate.

3. Placeyourhandontopofthegeneratorwiththepalmofyourhandfacedown.

4. Have someone turn on the generator. You can do it yourself, but be prepared for the possibility of a mild and

harmlessshock.

5. Thisworksbestwithpeoplewithlong,finehaironlowhumiditydays.Ifsomeonecomesclose,theycouldbemildly

334

shocked.

6. Whenyouarefinished,turnoffthevandeGraaffgenerator,stepoffthecrate,anddischargetheconductingsphere.

Levitatingpiepan

1. Groundtheconductingsphere.

2. Placeanaluminumpietinontheconductingsphere.

3. Turnonthegeneratorandobservetheresult.

4. Trythiswithseveralpiepansstackedontopoftheconductingsphere.

5. Turnthegeneratoroffandgroundtheconductingspherewiththegroundelectrodetoremoveanyresidualcharge.

Positiveornegative?

1. Groundtheconductingsphere.

2. Turnonthegeneratorandbringtheelectroscopeneartheconductingsphere.Don’tbetotallysurprisedifyougeta

spark.

3. Rubtheglassrodwiththesilktoproduceanegativechargeontheglassrod.

4. Bringthenegativelychargedglassrodtothetopoftheelectroscopetoseparatetheleaves.

5. Bring the negatively charged electroscope near the van de Graaff generator and observe whether the leaves

separatefurtherormoveclosertogether.

6. Rubtherubberrodwiththewool(orfur)toproduceapositivechargeontheglassrod.

7. Bringthepositivelychargedrubberrodtothetopoftheelectroscopetoseparatetheleaves.

8. Bring the positively charged electroscope near the van de Graaff generator and observe whether the leaves

separatefurtherormoveclosertogether.

9. Based on the response of the electroscope, what do you conclude about the type of charge produced on the

conductingsphereofthevandeGraaffgenerator?

Neonbulb

1.TurnonthevandeGraaffgenerator.

2.Darkentheroom.

3.Bringasmallneonbulb(withnoelectricalconnectionstoeitherend)neartheconductingsphere.Ifyougettooclose,

some sparks will likely discharge harmlessly in your hand. If you prefer for this not to happen, you can rig up a

nonconductingholdertosupporttheneonbulbduringthisexercise.Becarefultoavoidsuddenmovesthatmightresult

indroppingthebulb.

4.Positiontheneonbulbparalleltotheflooronalinepointingtowardthecenteroftheconductingsphere.Moveitcloser

andfurtherfromthevandeGraaffandobserve.

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Figure97-2Lightinganeonbulbbyexposingittoanelectricfield.

5.Position theneonbulbparallel to the floorona linepointingperpendicular to thecircumferenceof theconducting

sphere,asshowninFigure97-2.MoveitcloserandfurtherfromthevandeGraaffandobserve.

6.Turnthegeneratoroffandgroundtheconductingspherewiththegroundelectrodetoremoveanyresidualcharge.

ExpectedResults

Sparkswilldischargethroughtheair.Longersparksaregeneratedifthevoltageishighandthehumidityislow.Best-case

sparklengthisshowninFigure97-3.

Figure97-3Sparklength.BasedondatafromA.D.Moore,Electrostatics:Exploring,Controlling,andUsingStaticElectricity

(NewYork:Doubleday-Anchor,1968).

WhyItWorks

Anelectricalmotordrivesanonconductingbeltthatseparatespositiveandnegativecharges.Negativechargesaredrawn

awayfromtheconductingmetalsphereatthetopofthedevice,leavingastaticpositivechargeonthesphere.Bringinga

neutralornegativelychargedobjectclosetotheconductingsphereresultsinadischargeintheformofalightning-likespark

throughtheair.Themaximumlengthofthesparkdependsontherelativehumidityintheair.Asaruleofthumb,thespark

jumpsabout1centimeterforevery10,000voltsthatbuildup.

Objectsthatcomeintocontactwiththeconductingsphere,themselvesbecomecharged.Thiscausesrepulsionbetween

piecesofpapertapedtotheconductingsphere,ofthehairofapersontouchingthesphere(whilestandingonaninsulating

surface),andbetweensmallobjects,suchasStyrofoamchipsorRiceKrispiesthatcomeintocontactwiththesphere.

336

OtherThingstoTry

Chargesseparatedby thevandeGraaffgeneratorcanbeconcentratedon thebulbofanelectroscope.Thesignof the

chargecanbedeterminedbyobserving theeffectofachargedrodbroughtnear thebulb. If thecharge is thesame, the

leaves of the electroscope are driven further apart. If the charge is different, the leaves are drawn closer together. A

positivelychargedrodresultsbyrubbingwoolorfuronrubber.Anegativelychargedrodresultsbyrubbingsilkonglass.

Useofateslacoil isanotherway togeneratesparks that jump through theair.Thesecanbepurchasedashand-held

units.

ThePoint

Thisexperimentshowshow, through themovementofdissimilarmaterialsagainsteachother,staticelectricchargescan

buildup.Anelectricfieldisestablishedintheregionseparatingtheelectricalchargeswhichcanforcetheelectronstomove.

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Project98

TheWimshurstmachine.Separatingandstoringcharges.

TheIdea

The Wimshurst machine, like the van de Graaff generator, is capable of throwing long sparks as much as several

centimeters between two small conductive spheres. The Wimshurst machine is usually also tied to a Leyden jar, which

presentsagoodopportunitytoexplorecapacitanceandchargestorage.

WhatYouNeed

Wimshurstmachine

Method

1. CAUTION:Electricalcircuitryincludingpacemakers,hearingaids,cellphones,flashdrives,electroniccardoorlocks,

andcomputersmaybedamagedbythesparksgeneratedinthisexperiment.Inaddition,followallsafetyinstructions

providedbythemanufacturerofthisdevice.

2. SettheWimshurstapparatusonatable.

3. Darkentheroom.

4. Makesureallelectricaljumpersareinplaceforyourparticularsetup.Checkwiththemanufacturer’sinstructionsto

makesuretheapparatusissetupproperlywithcorrectelectricalpathstotheLeydenjarsanddischargespheres.

YoucandothisbothwiththeLeydenjarsconnectedornotconnectedtoyourcircuit.

5. Separatethetwodischargespheresbymorethan8cm.

6. Turnthehandleforfivesecondsorso,asshowninFigure98-1.

7. Holdingonlytheinsulatedwoodenhandlesforthedischargespheres,slowlybringthemtogether.

8. Notethedistancebetweenthedischargesphereswhenthefirstdischargeoccurs.

9. Setthedischargespheresatroughlythesameslightlycloserandslightlyfurtherdistances.

10. IftheLeydenjarswereinyourcircuit,repeattoseewhathappenswhentheyarenotconnected.

11. Touch the two spheres together for a few secondswhen finished tomake sure no residual charges are on the

electrodes.

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Figure98-1ChrisAleodemonstratestheoperationofaWimshurstmachine.

ExpectedResults

Withthedischargedspheresseparatedbyalargedistance,nothingshouldhappen.

Asthespheresapproachtowithinafewcentimetersseparatingthem,alightningboltwilljumpacrossthegap,asshownin

Figure98-2.

WhyItWorks

TheWimshurstmachineisconstructedfromtwoparallelplatesmadefrominsulatingmaterialsuchasLuciteorglass.The

platesarearrangedtobeturnedbyhandinoppositedirections.Narrowmetalstripsaremountedontheplatesandoriented

along the radius. Charges are transferred bymetal brushes that sweep across themetal strips as the plates rotate. In

contrasttothevandeGraaffgenerator,theWimshurstmachineseparateschargebytheprincipleofinductionratherthan

friction.Positiveandnegativechargesaccumulate,andtheycaneitherchargeaLeydenjarordischargeacrossagap.

Figure98-2Wimshurstmachineelectricaldischarge.

OtherThingstoTry

Charges separated by the Wimshurst machine can be determined using an electroscope, as described in the previous

experiment.

ThePoint

339

Thisexperimentshowshow,throughthemovementoftwoinsulatingplatesneareachother,staticelectricchargescanbuild

up.Theseparatedchargescanbestoredordischargedacrossasmallnonconductivegap.

340

Project99

Runningintoresistance.Ohm’slaw.

TheIdea

Ohm’s law forms thebasis for understanding howelectricity flows throughcircuits.This isa very simple relationship that

involvesthreethings:1)thevoltageorthepushthatmoveelectronsthroughthecircuit,2)thecurrent(oramps),whichisa

measureofhowmuchelectricityisflowingthroughthatcircuitasaresultofthatpush,and3)theresistance(inohms),which

doesallitcantomakeitdifficultfortheelectricitytoflow.

Because of its simplicity, this experiment is a good one for you to discover the law for yourself, based on your

measurements.

WhatYouNeed

one100ohmresistorratedfor0.5watt(otherresistorvaluescanwork,buttheresistormustberatedtohandlethe

wattagethatwillbeappliedtoit;thewattageissuppliedbytheresistormanufacturerandisoftenmarkedonthe

resistor)

ammeter

voltmeter

DCpowersupply(orbattery)

wirestoconnecttobatteryterminals

Method

1. Connectacircuit,asshowninFigure99-1.ThisisacircuitconsistingofaresistorinserieswithaDCpowersupply

andanammeterwithavoltmeterconnectedbyjumperwirestoeachoftheendsoftheresistor.Adrawingcalledan

electrical schematic is shown in Figure 99-2. This is equivalent to Figure 99-1, but it shows the electrical

connectionswithoutregardtotheactualphysicallayoutofthecomponents.

2. TurntheDCpowersupplytozero.

3. Settheammetertoreadmilliamps.Setthevoltmetertoread0–10volts.

4. IncreasetheDCpowersupplytogiveavoltagereadingof0.2volt.

5. Readthecurrent.

6. Dothesamewithavoltageof0.4,0.6,and0.8volts.

7. Graphcurrentversusvoltage.Drawalinethatbestfitsthedata.Whatisthesignificanceoftheslopeoftheline?

8. Repeatthiswitha200anda300ohmresistor.

ExpectedResults

Foragivenresistor,thegreaterthevoltage,themorecurrentflows.

Asresistanceincreases,lesscurrentflowsforagivenvoltage.

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Figure99-1CircuitformeasuringOhm’slaw.

Figure99-2SchematicformeasuringOhm’slaw.

Voltageincreaseslinearlywithcurrent.Theslopeofthelineistheresistancethecurrentisflowingthrough.

WhyItWorks

Ohm’slawisgivenbyvolts=resistance(ohms)×current(amps).Fromthis,youcanseethattheslopeofthevoltsversusthecurrentgraphisresistance.

OtherThingstoTry

Whathappensifyouhavetwoorthreeresistorsofthesameresistanceinarow,oneconnectedtothenext?Thisiscalleda

seriescircuitandisshowninFigure99-3.Foragivenvoltage,isthecurrentgreaterorlessthanforasingleresistor?

Whathappensifyoutakethosesamethreeresistorsandconnecttheminaparallelcircuit,asshowninFigure99-4?

ThePoint

Ohm’slawrelatesthevoltage,current,andresistanceofacircuit.Thevoltageatanyparticulartimeequalsthecurrenttimes

theresistance.

342

Figure99-3Measuringresistorsinaseriescircuit.

Figure99-4Measuringresistorsinaparallelcircuit.

343

Project100

Circuits:Bulbsandbuzzers.

TheIdea

Ifyouhaveneverbuiltacircuitbeforewithyourownhands,thisisyourchance.Likemanyoftheexperimentsinthisbook,

various levelsofcomplexityexistandyoucantaketheexperimentasfarasyoucareto.Youstartwithbuildingasimple

circuit, suchasmakingabell ring.Then, youbuildabasic telegraphsystem.Youbranchoutandaddseriesandparallel

pathstosimplecircuits.Next,youmeasurethecurrentandvoltageatvariouspoints inthecircuit.Finally,youlookathow

Ohm’slawcanbeappliedtomorecomplicatedcircuits.

WhatYouNeed

jumperwires

6Christmastreebulbs(orlow-voltagebulbsandsockets)

various(low-voltage)electricaldevicessuchasbells,buzzers,LEDs

DCpowersupply(orbatteryasinthepreviousproject)

knifeswitch

ammeter(ormultimetersetupasanammeter)

voltmeter(ormultimetersetupasanvoltmeter)

for the telegraph:5–10feetof insulatedwire, ironnail, twoblocksofwoodroughly3×6×¾ inches,asecondblockofwood¼inchtallerthanthenailafterbeingnailedintotheblock,a“tin”can,tinsnips,andafewsmallnails

Method

Buildingacircuit

1. LookatthecircuitdiagraminFigure100-1andmaketheappropriateconnections.

2. IfyouhaveanadjustableDCpowersupply,setavoltageof2–3voltsandkeepitconstantthroughoutthetest.You

mayneedtoadjustthis,dependingonthecircuityouareworkingwith.

3. Thecircuitdiagramshouldgiveyoualltheinformationyouneed.Hereareafewdetailsthatmaybehelpful:

–AttachajumperwiretothepositiveandnegativeterminalsoftheDCpowersupplyorbattery.(Notthattheelectrons

care,butredisgenerallyusedforpositiveandblackisusedfornegativeforclarityinassemblingthecircuits.)

–Theremustbeacompletepathfromthepositiveofthepowersupplyandbacktothenegative.

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Figure100-1Basicelectricalcircuitconsistingofabattery,bulbandaswitch.

–All connectionsmust bemetal-to-metal. If insulation is on thewires, youeither need to usea bare-metal alligator

connectororremovetheinsulation.

Makingatelegraph

1. Wind25–50turnsofinsulatedwirearoundalargeironnail.Leavethetwoendsofthewirefreeandremoveabout¾

inchofinsulation.

2. Hammerthenailintothewoodenblock.

3. Cuttwostripsfromyourcan,roughly2½incheslong×½inchwide.Bothpiecesshouldbeflexible.4. Attachoneofthemetalstripstothewoodenblock.Theheightofthewoodenblockshouldbe¼inchhigherthan

thenail.

5. Attachtheblockwiththemetalstriptothebaseblock,sothemetalisabovetheheadofthenail,butnottouching.

6. Buildthe“key”bynailingthesecondmetalstriptothesecondblockononeside,andthenputtinganailunderneath

theotherendofthemetalstrip.Leaveenoughofthenailheadexposedabovethewoodsurface,soyoucanwrap

wirearoundit.

7. OK.Let’shookeverythingup.WhatyouhaveisaseriescircuitfromtheDCpowersupplythroughtheelectromagnet

tothekey.Thekey issimplyaswitch.When itcloses, theelectromagnetpulls themetalstripdown,asshown in

Figure 100-2. Short and long durations are the dots and dashes of Morse code. If you have enough wire, you

separatethekeyandthereceiverbysomedistance.(Note:ifyouusethistocheatontestsinschool,pleasemake

sureyoudon’tsayyougottheideatodoithere.)

Seriesandparallelcircuits

1. AttacheachofthetwoendsofaChristmastreebulb(oralow-voltagebulbinasocket)acrossthepowersupply.

(Thismeans oneof thewires attached to the bulb goes to the positive terminal and the other end goes to the

negativelead.)

2. Connectthree(ormore)bulbsinseries.Comparethebrightnessofthesebulbswiththebrightnessofasinglebulb.

3. Connectthreebulbsinparallelandcomparewiththebrightnessofbulbsinaseriesandasinglebulb.

Measuringthecircuit

1.Repeattheprevioussetofmeasurements,butthistime,includeanammeterinserieswiththecircuitandavoltmeter

inparallelwith thecircuit,asshown inFigure100-2. It helpswith thecomparison if youkeep thevoltageconstant

throughoutthesemeasurementsandcomparethecurrentflowinginthecircuits.

2.Comparethecurrentflowingineachthesituations.

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Figure100-2Inatelegraphanelectromagnetisactivatedwhenaswitchisclosedtocompletethecircuit.

3.ApplyOhm’slaw(intheformR=V/I)tofindtheresistanceofeachofthecircuitsyoumeasured.

ExpectedResults

Currentwillflowinacircuitifacontinuouspathexistsfromthepositiveterminalofthepowersupplythroughallcomponents

ofthecircuit,andthenbacktothenegativeterminalofthepowersupply.

Componentsinseriesreducethecurrentthatcanflowbyeffectivelyaddingresistancetothecircuit.

Components in parallel result in increased current flowing through the circuit. The resistance of the overall circuit is

reducedwhencomponentsareaddedinparallel.

WhyItWorks

Whencomponentsareaddedinseries,thevoltageisdistributedoverallthecomponents.Asaresult,lesscurrentisableto

flow.

Whencomponentsareadded inparallel,alternatepathsareprovided for thecurrent to flowback to thebattery.Fora

givenvoltage,thepushfromthebatteryisabletoforcemorecurrentthroughthelargernumberofpaths.

OtherThingstoTry

Anextlogicalstepistocreateandtestmorecomplexnetworksofresistors.Thefollowingshowssomeexamples.These

canbeanalyzedusingthefollowingprinciples:

Resistorsinseriessimplyadd:Rseries=R1+R2

Resistorsinparalleladdinamorecomplexfashion.Resistorsinparallelcanbethoughtofasonesingleequivalent

resistancegivenby:1/Rparallel=1/R1+1/R2+…Thesecircuitscanthenbesimplifiedbycombiningseriesandparallelcircuits,andthenapplyingOhm’s law in its

variousforms(V=RI,R=VI,andI=V/R).

ThePoint

Ohm’s lawdetermineshowmuchcurrent (oramps) flows throughacircuit.Foragiven resistance (ohms), thegreater the

voltage,thegreaterthecurrent.

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Project101

Howdoesheataffectresistance?

TheIdea

Whenmatterheatsup,theatomsstartmovingfaster,likecarsinrush-hourtraffic.Thehotteritgets,themoredifficultitis

forelectronstomakeitthroughawire.Inthisexperiment,youexplorewhathappenswhenaconductorgetshot.

WhatYouNeed

one10-ohmresistorratedfor1Worgreater

DCpowersupplyorbattery

(optional) digital temperature sensor (some multimeters come with a thermocouple and setting to read the

temperature)

stopwatch

Method

1. Setupthecircuit,asshowninFigure101-1.

2. Attachthetemperaturesensortotheresistor.(Nottoworry.Ifyoudon’thaveathermocouple,thereisstillawayfor

youtodothis.)

3. Setavoltageofabout5V.

4. Measurethevoltage,current,andtemperature.

5. Continuetakingreadingsofvoltage,current,andtemperatureatregular intervals. Ifyoudon’thaveatemperature

sensor, you can still proceed, taking note of the fact that the resistor is heating up qualitatively. A relationship

betweenresistanceandtime(ratherthantemperature)canstillbeestablished.

6. UseOhm’slawtodeterminetheresistancebydividingthevoltagebythecurrent(inamps).

7. Whathappenstoresistanceastheresistorheatsup?

ExpectedResults

The higher the temperature, the higher the resistance. Resistance increases linearlywith temperature. See Figure101-2,

whichshowstheresistanceofa5centimeter(0.05m)sectionof20AWGcopperwireoverarangeoftemperatures.

WhyItWorks

Whenaconductor is heated, themoleculesmove inplacemore rapidly. Likeacarmovingonahighwaywith increasing

traffic,theelectronscannotmoveasfreelythroughtheconductor.Theresultistheresistanceincreases.

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Figure101-1Circuitformeasuringtheeffectofheatofresistance.

Figure101-2Resistanceversustemperaturefor5cmlengthof20AWGcopper.

OtherThingstoTry

Useanexternalsourceofheat,suchasahotplateoraBunsenburner,toheatthe(uninsulated)wire.

Use ice, dry ice, or liquid nitrogen to produce low temperatures. Your thermocouple may not read over the entire

temperaturerangeofyoursample,butyoucanstillobtainsomeextremelylow-temperaturereadingsasthesamplewarms.

ThePoint

Electricalresistanceincreaseswithtemperature.Thisrelationshipislinearoverabroadrangeoftemperatures.

348

Project102

Resistivity.Canironconductelectricitybetterthancopper?

TheIdea

Yes,ifthewireislongerorthicker.Copperiswellknownasagoodconductorofelectricity.Thissameisnotusuallysaid

aboutiron.Thisprojectdealswithtwoideasthatsoundsimilar,butthatarequitedifferent:resistanceandresistivity.

WhatYouNeed

uninsulatedcopperwire25cminlength

uninsulatedironwire25cminlengthofthesamediameter(thiscanbeindicatedbythewiregaugeorAWG)

(othermaterialcombinations,suchasaluminumorsilverwirecanbeusedinsteadof,orinadditionto,copperand

iron)

DCpowersupply

ammeter

voltmeter

(ifyouhaveadigitalmultimeter,youmaybeabletousetheohmmetersettingdirectly)

connectingwire

ruler

Method

1. SetupthecircuitasshowninFigure102-1.MarkthewirewithaSharpiein2cm(orotherconvenient)lengths.

2. Theammeterisattachedacrosstheentirelengthofthewire.Thecurrentfromthepowersupplyflowsthroughthe

entirelengthofthewire.Thevoltmeterisattachedonlyacrosstheselectedlength(2cm,4cmandsoon).

3. Readvoltage,current,anddistance.

4. Find the electrical resistance fromOhm’s law by dividing the voltage (volts) by the current (amps). This gives a

resistancereadinginohms.Thiscanalsobedirectlyreadfromanohmmeterifyouhaveone.

5. Comparetheresistanceyoumeasurefordifferentlengths.

6. Foragivendiameter,multiplyingtheresistancebythelengthgivesameasureofthewire’sresistivity.Whatdoyou

findhappenstothisvalueasthelengthincreases?

ExpectedResults

Thelongerthewire,thegreatertheresistance.

Thegreaterthecross-sectionalareaofthewire,thelowertheresistance.

Resistanceincreases(linearly)withlength.

Resistanceisinverselyproportionaltocross-sectionalarea.ThisisrepresentedinFigure102-2.

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Figure102-1Circuitformeasuringresistivity.

Figure102-2Resistanceofvariouslengthsofcopperwire.

Thecross-sectionalareasofthevariousAmericanwiregauges(AWG)areshowninTable102-1.

Table102-1

Resistivity at 20 degrees C for various materials used to make wires is shown in Table 102-2. This tells howmuch

resistanceiscontributedbyeverymeterofwire.

Table102-2

350

WhyItWorks

Foragivenwiresize,resistanceisproportionaltothematerial’sresistivity,accordingtotheequation:

R=ρL/AwhereRisresistanceinohms

ρistheresistivityinohm-cm(ρistheGreekletter“rho”)Lislengthincentimeters

Aiscross-sectionalareaincentimeters.

OtherThingstoTry

Alessprecise,butpossiblymorefun,approachtothisexperiment istousewirescutfromfooditems,suchaspicklesor

fruit,orbyformingwiresfromPlayDough.

Thewirecanbeslicedinsectionsasitismeasuredtoshortenitslength.Thisapproachmayrequiretheuseoftwometers

becausetheohmmetermaynotbestable.

Thiscanbetakenastepfurtherbycomparingtheresistancetotheresistivity.Youcangettheresistivitybymultiplyingthe

resistancebythelengthofthewire(incm)andtheareaofthewire(incm2).Youcangettheareaofthewirefromusinga

measuredorlooked-upvalueforthewirediameterandusingtheequation:

A=πr2

whereristheradiusofthewire.

ThePoint

Resistanceisameasureofhowdifficultitisforagivenvoltagetoforceelectronsthroughaconductor.Itdoesn’tmatterhow

bigorsmallthepieceofconductor.Allthatmattersistheoveralleffectithasintheelectricalcircuit.

On theother hand, resistivity is ameasure of how effective a particularmaterial is in impeding the flow of electrons.

Resistivityisthesameforanyparticularmaterial.

Resistancecombinestheeffectofthematerial’sresistivity,aswellasitslengthandcross-section.

351

Project103

Storingcharge.Capacitors.

TheIdea

Acapacitor isanelectroniccomponent thatcanstoreanelectricalcharge.Unlikeabattery thatstoreselectricalcharge

throughchemical reactions, thecapacitorholdselectronsonconductiveplatesseparatedbyan insulator.Capacitorsare

present in numerous electronic circuits. They are also gaining attention recently as a possible means of supplementing

batteriesinelectriccars.Thisexperimentexploreshowcapacitorscanbechargedanddischarged.

WhatYouNeed

1000μF(micro-Farad)capacitor50kΩ(kilo-Ohm)resistor(noteothercapacitor/resistorcombinationsthatcanworkarelistedinTable103-1)DCvoltmeter(ormultimeterconfiguredasavoltmeter)

10-voltDCpowersupply

DCammeter(with0–1.0mArange)

3knifeswitches(SW1,SW2,andSW3)

jumperwire

stopwatch

2LEDs

Method

Charging

1.SetupthecircuitshowninFigure103-1.Payattentiontothepositiveandnegativepolaritymarkings,especiallyifyour

capacitorhasadesignatedpositiveside(somedoandsomedon’t).Startwithallswitchesopen.

2.CloseSW2.LeaveopenSW3.

3.CloseSW1andstartthetimer.

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Figure103-1Circuitforstudyingcapacitors.

4.RecordthecurrentinmAeveryfiveseconds(thisiseasierwithpartners).Ifyoumissareading,keepgoingandcatch

the next five-second interval. Keep going until the current becomes too small to read. If other capacitor/resistor

combinationsareused,adifferenttimeintervalthanfivesecondsmaybemoreappropriate.

Discharging

1. Whenthechargingpartiscomplete,openalltheswitches.

2. CloseSW1andleaveSW2open.

3. CloseSW3andstartthetimer.

4. Asbefore,recordthecurrentinfive-secondintervals.

ExpectedResults

With SW2 closed, the capacitor will charge. LED2 will light, but slowly fades as the voltage builds and the current flow

decreases.For the10kΩ resistorand the1000μFcapacitorgiven in theparts list, thechargingwillbeabout two-thirdscompletein50seconds,asshowninFigure103-2.

WithSW3closed,thecapacitorwilldischargeasindicatedinFigure103-3.After50secondsthevoltagewillhavedropped

from10voltstoaround3.7volts.LED3willlightandwillslowlyfadeasthecapacitordischarges.

353

Figure103-2Capacitorvoltageversustimefora1000μFcapacitorchargingthrough10kΩand50kΩresistors.

Figure103-3Capacitorvoltageversustimefora1000μFcapacitordischargingthrough10kΩand50kΩresistors.Ingeneral,thetimetochargeordischargetwo-thirdsofcapacityischaracterizedbythetimeconstant.ForacapacitorC

(inFarads)andaresistorR(inohms),thetimeconstant,τ(inseconds),isgivenbyτ=RC.Thetimeconstantrepresentsthetimewherethecurrentduringchargingor thevoltageduringdischarginghasdecreasedbyabout two-thirds.Thefollowing

combinations of resistor and capacitor (Table 103-1) give a reasonable time constant of 30 seconds, which gives

measurableresultsinthisexperiment.

Table103-1

354

WhyItWorks

ThecurrentforachargingcapacitorisgivenbyI=Ioe−t/RC

ThevoltageforachargingcapacitorisgivenbyV=Vo(1–e−t/RC)

ThecurrentforadischargingcapacitorisgivenbyI=Ioe−t/RC

ThevoltageforadischargingcapacitorisgivenbyV=Voe−t/RC

Whent=thetimeconstant,RC,thene−t/RC=e−1=0.37.Thismeanadischargingcapacitorhasdroppedtoaboutone-

thirdofitsoriginalvalueorhasdischargedabouttwo-thirds.

OtherThingstoTry

Ifyouhaveotherresistorsandcapacitorsavailable,try(small)increasesordecreasesinvalues,andthendeterminehowit

affects the time to charge and discharge. The previous Table 103-1 gives combinations that result in reasonable time

constantsandservesasagoodstartingpoint.Adjustyourmeasurementintervalasneeded.

Usea current and voltage sensor that displays theseparametersasa functionof timeona computer. A combination

voltage/current sensor (part number PS-2115) is available from PASCO that displays both parameters simultaneously in

DataStudiosoftware.

Makeagraphof voltage (orcurrent) versus time for yourdischargedatawith voltageona linearscaleand timeona

logarithmicscale.UseanexponentialcurvefittoanExcelscatterplottofindtheargumentoftheexponent.Comparethat

with–1/RC.

ThePoint

A capacitor is a device that stores electrical energy. The rate of charging and discharging depends on the size of the

capacitorandtheresistorit ischargingordischargingthrough.Thebiggerthecapacitorandtheresistor,thelongerthese

processestake.Thecharginganddischargingisanexponentialfunctionoftimethatapproachesasaturationvalue.

355

Project104

Isthemagneticforcemorepowerfulthangravity?

TheIdea

Inthisexperiment,youuseamagneticfieldtodefygravityandholdamagneticobjectsuspendedintheair.Youalsoexplore

theeffectivenessofvariousmaterialsinshieldingtheeffectsofthemagneticfield.

WhatYouNeed

powerfulpermanentmagnet

ringstandwithclamp

paperclip

12inchesof(lowmass)string

materialstotestasashield:glass,paper,copper

pieceoftape

Method

1.Securethemagnettotheringstand,sothemostpowerfulmagneticfieldisdirecteddownward.

2.Tiethestringtothepaperclip.

3.Bringthepaperclipneartheoverheadmagnet.Itshouldbecloseenoughforthemagneticfieldtoexertaforceon

theclip,asshowninFigure104-1.

4.Tapetheotherendofthestringtothetable.Usingtapeenablesyoutoeasilymakeslightadjustmentsinthestring

length.

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Figure104-1PhotobyS.Grabowski.

5.Atthispoint,ifyouaregoingtoshowthistosomeone,thiswouldbeagoodpointtohavethemcomeintotheroom.

6.Observewhathappenswhenyoubringthepaperclipcloser,andthenfurtherfromthemagnet.

7.Tryblockingthemagneticfieldbyusinganyofthefollowingpotentialshieldingmaterials:glass,paper,copper,iron.

ExpectedResults

Thepaperclipappearstodefygravityandwillbeheldsuspendedabovethetable.Dependingonthestrengthofthemagnet,

agapofafewmillimeterscanbeestablishedbetweenthepaperclipandthemagnet.

Themagneticfieldcanbeshowntopenetratethroughmaterials,suchasglass,paper,wood,orcopper.SeeFigures104-

2and104-3.

357

Figure104-2Doesamagneticfieldpassthroughaconductor?Thisshouldleavelittledoubt.PhotobyS.Grabowski.

Figure104-3Doesamagneticfieldpassthroughaninsulator?PhotobyS.Grabowski.

WhyItWorks

358

Theforceexertedbythemagnetisgreaterthantheforceofgravity.

OtherThingstoTry

Useaverysensitivespringscaleoraforcegaugetomeasurethemagneticforceexertedonthepaperclip.

ThePoint

Magneticfieldsexertaforceonmagneticobjects.Thisforcedecreaseswithdistance.Themagneticfieldpenetratesboth

electricalinsulatorsandconductors.

359

Project105

Magneticlevitationusinginduction.Electromagneticringtosser.

TheIdea

Thisisafundemowithsomewhatsurprisingresults.Youwilluseapowerfulmagneticfieldtoexertaforceonamaterialthat

is not normally magnetic. You will generate a circulating current using electromagnetic induction. The result is that the

magneticrepulsioncausesametalobjecttobeforcefullythrownintotheair.

WhatYouNeed

ringlauncherapparatus(ElihuThomsonapparatus).PicturedinFigure105-1isPASCOEM-8661.

coppercollar

aluminumring

splitaluminumring

copperring

Figure105-1CourtesyPASCO.

leadring

coilofinsulatedwireconnectedinserieswithalow-wattagelightbulb

ACvoltmeter(ormultimeterconfiguredasanACvoltmeter)

tongs

optional:Pyrexbowlwithliquidnitrogen

Method

1. Safety:Allwiringtothelaunchershouldbeappropriatelyenclosedandinsulatedtoavoidapotentialshockhazard.

Without giving away the results of this experiment yet, it should come as no surprise thatmetal objects will be

launched, sometimes at significant velocities.Make sure no one and nothing of value can be hit by flying rings.

Cautionshouldbeexercisedwhenworkingwithlow-temperaturerings.Avoidconstraininganyofthecollarsforany

prolongedperiod,whichcouldresult inelevatedtemperaturesandburninghazard.Thecurrentshouldflowthrough

thecoilofthelauncherforalimitedtime.Becarefultoavoidoverheatingthecoilbyflowingcurrentforanexcessive

360

time.

2. Slidethealuminumringovertheironcoreoftheringlauncherapparatusandslideindownoverthecoil.

3. Activatethelaunchswitchforafewsecondstoapply120Valternatingcurrenttothecoil.

4. Repeatwiththeotherringsandcollars.

5. ConnectanACvoltmeteracrossthetwosidesofthesplitringtomeasurethecurrentwhilethecurrentisflowingin

thecoreofthelauncher.Similarly,putacoilofwirearoundthecore.ComparetheACvoltagedevelopedinone,two,

ormultiplecoilsofwire.

6. Placethecoilofwireattachedtothelightbulboverthelaunchercoilandapplycurrenttothelauncher,asshownin

Figure105-2.

7. Holdthecopperringoverthecollarforafewsecondswiththelauncherturnedonandfeelthecollar’stemperature.

(Becarefulnottoholdittoolongoritmaygettoohottohandle.)

8. For this next part, make sure the ceiling is high enough. Immerse the rings in liquid nitrogen and activate the

launcher.

ExpectedResults

Closedconductiveringsandcollarswillbethrowverticallybytheringtosser,asshowninFigure105-3.Thecopperring is

thrownthehighest,followedbyaluminum.Thecoppercollarisraised,butitismoresluggish.Thesplitringsarenotlifted.An

ACvoltageofafewmillivoltscanbemeasuredacrossthesplitring.Aringthatishelddownwhilethecurrentisflowingin

thecoilwillheatupsignificantly.Theringscooled in liquidnitrogenaremuchmoreresponsethantheir roomtemperature

counterparts.Thecooledcopperringwillflythehighestandcanlikelydamageastandard8to10foot(2meter)ceiling.The

lightbulbwillbeilluminatedwhenheldoverthecurrent-carryingcoil.

Figure105-2Inducedcurrentcauseslighttobeilluminated.CourtesyPASCO.

WhyItWorks

This is a demonstration of electromagnetic induction based on an apparatus developed by the prolific inventor Elihu

Thomson.Aconstantlychangingmagneticfieldproducedbytheappliedalternatingcurrentcausesanopposingcurrent,and

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voltageintheringsandcollars.ThegenerationofanopposingcurrentisanillustrationofLenz’slaw.

Figure105-3Ringtosser.CourtesyPASCO.

Thisinducedcurrentgivesrisetoamagneticfieldorientedtorepelagainstthefieldthatformsintheringlaunchercoils.

Therepulsionbetweenthesemagneticfieldscausestheringtobetossed.

Becausecopperisabetterconductorthanaluminumorlead,morecurrentflowsandtheringistossedhigher.Thecollars

areheavierandarenotthrownasfar.Thesplitringsdonotprovideacompletecurrentpath,sotheinducedcurrentdoesnot

flowinacompletecircuit.Thebulblightsbecauseacurrentisinducedinthecoilconnectedtothebulb.Theliquidnitrogen

reduces the resistance of the rings.With lower resistance,more current can flow. The higher current creates a stronger

magneticfield,whichlaunchestheringhigher.

OtherThingstoTry

ThecurrentgeneratedinthesplitringcanbemeasuredbyattachinganACvoltmeteroramultimeterconfiguredasanAC

voltmeter.

ThePoint

Acurrentflowinginaconductorproducesamagneticfield.Achangingmagneticfieldcaninduceacurrentinaconductor.

Theinducedcurrentcanthengenerateacurrent.ThesecurrentsaccordingtoLenz’slawwillalwaysopposeeachother.

362

Project106

Magneticlevitationusingsuperconductivity.TheMeissnereffect.

TheIdea

Typically,whenthetemperatureofaconductorisreduced,theresistanceisalsolowered.Wesawinthepreviousexperiment

howamagnetic field cancauseanobject to levitate. For somematerials, ifwecontinue to lower their temperature, the

resistancecontinues todropuntil itdisappearsentirely.When thishappens,wehavewhat isknownasasuperconductor.

Superconductorshaveamazingpropertiesandarebeginningtofindtheirwayintopracticalapplications.

WhatYouNeed

liquidnitrogen

thinpieceofcork(about¼inchthick)

Styrofoamdish(formedbycuttingaStyrofoamcup;tThetotalheightshouldbeabout2mm)

cube-shapedneodymiummagnet(seeFigure106-1)

plastictongs

superconductordiskconsistingofYBa2Cu3O7ceramic(seeFigure106-2)

optional:videocameraorPCcamconnectedtoaTVmonitor(toshowthistoalargergroup)

optional:thermocouple,voltmeter,DCpowersupply,superconductorcoil,superconductorsamplewithmeasurement

leadsattached

Figure106-1Neodymiummagnetcube.

Figure106-2YBa2Cu3OO7ceramicdisk.

363

Method

1. PlacetheYBa2Cu3O7ceramicdiskonthetableandsettheneodymiummagnetontopof it toshownorepulsive

forceisoccurringatroomtemperature.

2. PlacethecorkinthecenteroftheStyrofoamdish.

3. PlacetheblackYBa2Cu3O7ceramicdiskonthepieceofcork.

4. CarefullypourliquidnitrogenintotheStyrofoamdishtopartiallycovertheceramicdisk.

5. Theliquidnitrogenwillboilforashortwhile.Whentheboilingsubsides,thediskhassufficientlycooled,asshownin

Figure106-3.

6. Usingtheplastictongs,pickuptheneodymiummagnet.Carefullyplacethemagnetovertheceramicdisk.

7. Whenthemagnetisobservedtohoverovertheceramicdisk,usethetongstogiveitaspin,asshowninFigure106-

4.

8. Becausethepartsinthisprojectaresmall,iftheintentionistoshowthistoalargergroup,avideocameraorPC

camcanbeusedtodisplaythisonamonitor.

ExpectedResults

Themagnet is held suspendedabove the ceramic superconductingmaterial. If themagnet is spun, it continues spinning

withoutnoticeableresistance.Eventually,theceramicwillwarmupandthesuperconductingeffectwillfade.

Figure106-3SuperconductingdiskbeingbroughtbelowCurietemperature.

364

Figure106-4Magneticcubespinningabovesuperconductingceramicdisk.

WhyItWorks

Normally,attemperaturesabovewhat isknownasthecriticaltemperatureofamaterial, thematerialhassomeelectrical

resistance. This means a voltage must be applied across the material to push the electrons through the material. The

voltageisneededtodrivetheelectronsthroughwhatislikeanatomicobstaclecourse,consistingofotheratomsvibrating

randomly.As(normalnonsuperconducting)resistorscooldown,theirresistancegetslower.However,superconductorshave

zeroresistance.Notjustlower,butzero!Thismeanstheelectronsnolongerneedavoltagetopushthem.Thisalsomeans

theelectronscanmoveaboutfreelythroughoutthesuperconductorwithoutenergylosses.

Differentmaterialsbecomesuperconductingatcharacteristictemperaturesthatdifferforeachmaterial,asshowninthe

followingtable:

Noticethatall themetals listedmustbecooledtobelow4.2K.Toaccomplishthis, it isnecessarytouseliquidhelium,

whichremainsliquiduptothattemperature,asshowninthefollowingtable. In1987,abreakthroughwasachievedbythe

discoverythatYBa2Cu3O7ceramicbecamesuperconductingaround90K(andbelow),whichcanbeachievedbyimmersion

inliquidnitrogen.Thisisfarlessexpensiveandeasiertoworkwiththanliquidhelium.Scientistsarepursuingmaterialsthat

canbesuperconductingattemperaturesclosertoroomtemperature,whichcouldopenthedoortoitsapplicationinmany

newareas.

TheactualdetailsofhowsuperconductivityworkswilltakeusfurtherintoquantummechanicsthanIthinkmostreaders

would care to go. The theory known as BCS theory was named after three American physicists: Bardeen, Cooper, and

Schrieffer. (Very) basically, theBCStheory describes how electrons are able tomore easily navigate through the crystal

latticeofmatter in amanner that is somewhat analogous toa racecar encountering lessaerodynamic resistanceas it

closely follows another car in front of it. As the critical temperature is reached, the electrons are able to go through a

materialby“tunneling”rightthroughanelectricalfieldinitsway.Asaresult,superconductorshavezeroresistance.Ifdigital

electronicswerebasedonsuperconductorstheywouldfunctiontentimesfasterthanstandardsemiconductorelectronics.

Magnetic fields can pass through and be present in most materials, including superconductors above their critical

365

temperature.However,asasuperconductingmaterial isbroughtbelowitscriticaltemperature,themagneticfield isforced

out in a process known as the Meissner effect, which serves as the basis for the effect we saw here. To enable the

magnetic field to be pushed out of the superconductor, it becomes necessary for a counter current to flow in the

superconductor.Withnoresistance,electricalcurrentsareinducedinthesuperconductingceramic,which,inturn,createsa

magneticfieldthatrepelsagainstthatofthepermanentmagnet.

Superconductorsarebeinglookedattoaddresssomeofthefollowingchallengesintechnology:

1. Muchoftheelectricalpowertransmittedthroughouttheworld’selectricalpowergridisdissipatedasresistiveheat

losses. If superconductors could be used for power transmission and generation, some of the losses could be

reduced.

2. Magneticresonanceimaging(MRI)equipmentusesextremelypowerfulmagnetstohelpcreatedetailed imagesof

thebody.Superconductorsallowstrongermagnetstobebuilt.

3. Maglev trains use superconductors to help produce powerful magnetic fields that raise trains above the track,

enormouslyeliminatingfriction.

4. Theextremelypowerfulmagnetsusedtoguidebeamsofsubatomicparticlesinresearchfacilities(suchasCERN)

usesuperconductors.

5. Superconductorsholdthepromiseofenablingfasterprocessingofdigitalinformationincomputers.

OtherThingstoTry

Someadditionalexperimentsinclude:

Measurethecriticaltemperature

Attach a thermocouple to the superconductor tomeasure the critical temperature. This is the temperature at which the

magnetfirstbeginstolevitateaboutthecooledceramicdisk.Thethermocoupleshouldnotconstrainthemagnetfrombeing

liftedandshouldnotbeimmersedintheliquidnitrogenoritwillunderstatethecriticaltemperature.

Resistanceversustemperaturecurve

BasicallytodothisyouwilluseOhm’slaw(resistance=voltage/current)tomeasuretheresistanceofthesuperconductoras

itstemperaturechanges.Itiseasiertomeasurethesechangesasthesuperconductorwarmsfromtheinitialimmersioninto

liquidnitrogenuntilitpassesthroughthecriticaltemperature.Twowiresforcurrentandtwowiresforvoltageareattachedto

the superconductor. This is called a four-point probe, which eliminates the effect of contact resistance that would be

encounteredifbothvoltageandcurrentweremeasuredusingasinglesetofcontacts.Thecontactscanbeformedusing

very high gauge (thin) silver or copper wire and attaching them to the superconductor using silver paint. A sample with

contactsattachedcanbeobtainedaspartofanexperimentkitbysuperconductorexperimentsuppliers.

ThePoint

Superconductors arematerials that have no electrical resistancewhen they are brought below their critical temperature.

SuperconductorscanexertofforceonapermanentmagnetasaresultoftheMeissnereffect,inwhichacirculatingcurrent

is established in response to exclusion of the magnetic field. This current generates a magnetic field that repels the

permanentmagnet. Superconductors have significant technological applications, includingMRIs,maglev trains, subatomic

particleresearch,andultrafastdigitalelectronics.

366

Project107

Movingelectronsproduceamagneticfield.Oersted’sexperiment.Themagneticfieldof

acurrent-carryingwire.

TheIdea

Whatcausesamagneticfield?In1820,HansOersteddiscoveredthatelectricityflowinginawirecausedacompassneedle

tobedeflected.Thisestablishedoneoftheearliestconnectionsbetweenelectricityandmagnetism.Thisinvestigationre-

createssomeofthethingsOersteddid.

WhatYouNeed

DCpowersupplyorbattery

aboutameter(afewfeet)ofinsulatedwire

compass,preferablyonemountedonapivot

ringstandorothersupportforthewire

optional:ammeter

optional:knifeswitchtocompletethecircuit.Youcanactivatethecircuitsimplybycompletingthefinalconnection

tothepowersupply.

Method

1.Connectoneendofthewiretothepositiveterminalofthepowersupply(orbattery).

2.Routethewirethroughthesupport,soalengthofabout0.25m(oraboutafoot)isrunningupanddown.Thecurrent

flowingfromthepositiveterminalshouldflowupthroughthewire.

3.Theothersideofthewireshouldeithergotooneoftheterminalsoftheswitchorbeplacedreadytoattachtothe

negativeterminal.Ifyouareusingtheknifeswitch,keeptheswitchintheopenpositionandattachtheotherterminal

tothenegativeterminal.

4.Makesurenoothermagnetsareintheimmediatevicinityoftheapparatus.

5.Placethecompassclosetothewire.(ThecompasswillpointinthedirectionoftheEarth’smagneticfield.Imaginea

circleformedaroundthewirewhenviewedfromabove.Toexperiencetheforcegeneratedbythemagneticfieldof

thewire,thecompassneedleshouldnotbeatatangenttothatcircle,butitshouldformsomeangletothetangentat

thatpoint.ThisisshowninFigure107-1.)

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Figure107-1Measuringtheeffectofcurrentonamagnet.

6.Completethecircuit(eitherbyclosingtheswitchorbyattachingthewiretothenegativeterminal).Ifyouareusingan

adjustablepowersupply,itmaybehelpfultoputanammeterinserieswiththepowersupplytomakesurethecurrent

flowdoesn’tgomuchabove1amp.Thiscanalsoletyouquantifytheeffectofincreasingcurrentonthestrengthof

thegeneratedmagneticfield.

ExpectedResults

Withacurrent flowing through thewire, thecompass isdeflected.Themagnetic fielddeflects thecompassneedle in the

directionofthetangentofthecircle,asshowninFigure107-1.

WhyItWorks

Amagneticfieldisproducedbymovingelectriccharges.

OtherThingstoTry

Measuretheeffectofincreasingthecurrentandmovingthecompassfurtherfromthewireontheresponseofthecompass

needle.

ThePoint

Anelectricalcurrentflowinginaconductorproducesamagneticfield.

368

Project108

Faraday’sexperiment.Currentgeneratedbyamagnet.

TheIdea

MichaelFaradaydiscoveredthatamovingmagneticfieldcausesanelectricalcurrenttoflowinawire.Mostoftheelectricity

generatedthroughouttheworldtodayisbaseduponthishistoricdiscovery.Powerplantsroutinelyconvertmechanicalenergy

intoelectricalenergy.Thisexperimentexploresthephysicalprinciplethatmakesthispossible.

WhatYouNeed

barmagnet

coilof insulatedwire—themorecoils, themorepronounced theeffect.Thin “magnet”wire insulatedwithclearor

coloredenamelcanworkfine.

galvanometer(averysensitiveammeter)

Method

1. Wraptheinsulatedwireinacoilaroundacylindricalcardboardform.Usethesmallestdiameterthatwillenablethe

barmagnettopassthrough.Prewoundcoilsareavailable.

2. Connectthetwoendsofthewiretothepositiveandnegativeterminalsofthegalvanometer.

3. Predictwhatyouthinkwillhappenifthemagneticisplacedinsidethecoil.Tryitandobservetheresponseonthe

galvanometer.

4. Movethemagnetbackandforthinthecoil.Observethedeflectiononthegalvanometer.

5. Movethemagnetbackandforthoutsidethecoilandobservetheeffect.Whathappensifthecoilmoveswhilethe

magnetisstationary?

6. If it ispossibletoincreaseordecreasethenumberofcoils,youcanevaluateitseffectontheamountofcurrent

thatcanbegenerated.

7. Basedonyourobservations,describehowamagnetcanproduceanelectriccurrent.

TheapparatusisshowninFigure108-1.

ExpectedResults

Amagnetproducesacurrentinawireonlywhenthemagnetismoving.Astationarymagnetwillnotgenerateacurrent.

369

Figure108-1Amagnetmovingthroughacoilofwire.

Thefastertherelativemotionbetweenthemagnetandthecoil,thegreaterthecurrent.Thelargerthenumberofcoils—

withallelseequal—thegreaterthecurrent.Amorepowerfulmagnetproducesagreatercurrent.

WhyItWorks

Amagneticfield itselfdoesnotproduceanelectriccurrent.Achangingmagneticfield isrequiredtoproduceanelectrical

current.ThisisaddressedinmathematicaldetailbyMaxwell’slawsforthosewhowanttopursueitfurther.

OtherThingstoTry

Aniceway todisplay these results is toattach thecoil toavoltagesensoranduse this togenerateagraphofvoltage

versustime.Movingthemagnetbackandforthinthecoilresultsinanalternatingcurrent(AC).Ifyouhangthemagnetona

springandhaveitoscillateupanddowninthecoil,youwillhaveasimplemodelofanACgenerator.

Agoodfollow-upistoinvestigateamodelelectricalgenerator,whichcanalsogenerateasimilarACcurrent.

ThePoint

Thesignificanceofthisprojectistoshowhowmechanicalenergyisconvertedintoelectricalenergy.Thekeypartsofan

electricalgeneratorareamagnetandacoilofwire.Electricityflowswhenthecoilandmagnetmoverelativetoeachother.

370

Project109

Ifcopperisnotmagnetic,howcanitaffectafallingmagnet?Lenz’slaw.

TheIdea

Whenamagnetmovesnearaconductor,electricalcurrentscanbeproducedintheconductor.Whencurrentscirculateina

pieceofbulkmaterial, ratherthanawirethatformsacompletecircuit, thecurrentsarecallededdycurrents.Theseeddy

currentsaremorelikewaterswirlinginatidepoolratherthanflowinginastream.Eddycurrentscanreducetheefficiencyof

electrical devices, such as transformers, because the circulating current results in a loss of power. Eddy currents have

severaluses,which includemagneticdampingofsensitivemeters,andtheyareused inmagneticbrakingforrapidtransit

trains.ThisprojectexploresanaspectofeddycurrentscalledLenz’slaw.

WhatYouNeed

3neodymiumdiscmagnets

copperpipewhosediameterisslightlylargerthanthemagnet

plasticpipeofsimilardimensions

Method

1. Holdbothpipesvertically.

2. Checkthemagneticattractionbetweenthemagnetsandeachofthepipes.

3. Positionthemagnetovertheopentopofeachofthepipes.

4. Dropthemagnetthroughthepipesatthesametime.

5. Comparehowfastthemagnetsfallthrougheachofthepipes,asshowninFigures109-1and109-2.

ExpectedResults

Themagnetfallsthroughtheplasticpipefasterthanthroughthecopperpipe.

371

Figure109-1Bothmagnetsaredroppedatthesametime.Thenon-conductivetubeisontheleft.

372

Figure109-2Themagnetgoingthroughthenon-conductivetube(ontheleft)emergesfirst.

WhyItWorks

Whenamagnetmoveswithrespecttoaconductor(suchascopper),itcreates(induces)anelectriccurrentintheconductor.

Thiscurrent,inturn,producesamagneticfield.AccordingtoLenz’slaw,thismagneticfieldwillbealignedinsuchawaythat

it is pointed in the opposite direction as themagnetic field that originally produced it. This results in an attractive force

between themagnetand thecopperpipe inwhichacurrent is inducedby the fallingmagnet.Because theplastic is not

conductive,nomagneticfieldisproducedtocreatetheLenzeffect.

OtherThingstoTry

Oneotherway todo this is to usediscmagnetswith holes in their centers.Then, themagnetsareplacedover copper,

plastic,andironrodswhosediameterisslightlysmallerthantheinnerdiameteroftheholeinthemagnet.

Analuminumdisc isnotmagnetic. If thedisc isspunandastrongmagnet isbroughtnear,eddycurrentsareproduced

whoseeffect istoslowthespinningdisc.This isknownasmagneticbraking,and it isshowninFigures109-3andFigure

109-4.

ThePoint

Lenz’slawdescribeshoweddycurrentsareformedinanonmagneticmaterial.Theseeddycurrentsinteractwithamagnetin

awaythatopposestheeffectofthatmagneticfield.

373

Figure109-3Aneodymiummagnetisbroughtnearaspinningnon-conductingplate.

Figure109-4Magneticbraking(andnotfriction)stopstheplate.

374

Project110

Effectofamagnetonanelectronbeam.Theright-handruleformagneticforce.

TheIdea

OneofthegreataccomplishmentsofphysicsinthetwentiethcenturywasthediscoveryoftheelectronbyJ.J.Thomson.In

thisproject,yourevisitsomeofthestepsthatledThomsontohisdiscovery.

WhatYouNeed

cathode ray tube (CRT)—this can be any tube-type video monitor (TV or computer). If you have access to an

oscilloscope,youcanusethat.Liquidcrystaldisplay(LCD)orplasmascreendisplaysdonothaveelectronbeams

andwill notwork here. A stand-aloneCRT (such as aCrooke’s tube available from scientific supply companies

excitedbyaninductioncoil)canbeused.

strongmagnet

yourrighthand

miniPost-itnotes

Method

1.CAUTION:Ifyouareusingahigh-voltageinductioncoiltoproducetheelectronbeamintheCRT,beverycarefulnot

totouchtheexposedterminalswhileitisoperating.Becertainyouexactlyfollowthemanufacturer’s instructionsfor

usingthisequipment.

2.Careful:ItistypicallynotrecommendedtoexposeTVorcomputerscreenstomagneticfields.Excessiveorprolonged

exposurecancauseunintendeddamage.

3.TurnontheCRT.

4.Makeanyadjustmentsneededtofocustheelectronbeam.

–Foranoscilloscope,disabletheverticalandhorizontalsweeps,leavingasingledotatthefocus

–Withthecomputer,findapointoffocus,includingtextoraperiodonthescreen

–WiththeTV,findastationaryimagetofocuson

5.Identifythenorthpoleofyourelectronmagnet.

6.Bringthemagnetnear(butnottouching)theCRTscreen.

7.Observetheeffectofthemagnetontheelectronbeam.

ExpectedResults

Themagneticfieldcausestheelectronbeamtobend.

Ifthebeamismovingtoyourrightandthemagneticfield,northtosouth, ispointedinwardacrossthetube,theelectron

beamwillbebentdown.SeeFigure110-1.(Notethatsinceelectronshaveanegativecharge,thisistheoppositedirection

specifiedbytheright-handruleforpositivecharges.)

Figure110-2showsanelectronbeammovingfromlefttorightinacathoderaytube.Intheabsenceofamagneticfield,

thebeamishorizontal.

375

Figure110-1Effectofamagneticfieldonanelectronbeam.

Figure110-2Cathoderaytube.PhotobyS.Grabowski.

If a magnetic field is placed across the beam (with the north pole indicated by tape in front), the beam is deflected

downwardasshown(bySteveGrabowski)inFigure110-3.

Ifthemagneticfieldisreversed(sothatthenorthpoleisintheback)thebeamisdeflectedupwardasshowninFigure

110-4.

WhyItWorks

Amagnetic field does not exert a force on a stationary electron. However, amagnetic field does producea force on a

movingelectron.Theelectron’smotion,themagneticfield,andtheforceareallatrightanglestoeachother.

Figure110-3Cathoderaytubewithmagneticfieldfronttoback.

376

Figure110-4Cathoderaytubewithmagneticfieldbacktofront.PhotobyS.Grabowski.

OtherThingstoTry

Thedirectionoftheforceontheelectronfollowstheright-handrule.Ifyourindexfingerpointsinthedirectionofthebeam,

andyourotherthreefingerspointinthedirectionofthemagneticfield(northtosouth),thenyourthumbshowsthedirection

ofaforceonapositiveparticle (or theoppositedirectionforanegativeparticle,suchasanelectron).Youcan label the

fingersofyourrighthandwithPost-itnotestohelpkeeptrackoftheelectronmotion,thefield,andtheresultingforce.(This

iswhyPost-itnotesareontheWhatYouNeedlist.)

Youcantakethisastepfurther.Thomsonappliedanelectricfieldtodeflecttheelectronbeambyameasurableamount.

Then,byapplyingamagneticfieldatarightangletotheelectricfield,Thomsonwasabletodeterminethechargetothe

massratiooftheelectron.Thiscanbeperformedusingcommerciallyavailableequipment.

ThePoint

Propertiesoftheelectroncanbedeterminedbyobservingitsbehaviorinelectricandmagneticfields.

Theelectronisnegativelycharged.

Theforceproducedbyamagneticfieldonamovingbeamofelectronscanbedescribedbytheright-handrule, inwhich

thethumbindicatesthedirectionoftheforce,theindexfingerindicatesthedirectionofthemotionoftheelectrons,andthe

restofthefingersindicatethedirectionofthemagneticfield.

Carefulanalysisofelectricandmagneticfieldsonanelectronbeamdeterminesthechargetomassratiooftheelectron.

377

Project111

Whatistheshapeofamagneticfield?

TheIdea

Youcannotseeamagneticfield.Butyoucandefinetheshapeofthefieldbymeasuringitseffects.Inthisproject,youtrace

theshapeofthemagneticfieldcreatedbyvariousarrangementsofpermanentmagnets.

WhatYouNeed

2barmagnets

U-magnet

severalsheetsofpaper

ironfilings

Method

1. Laythebarmagnetonthetable.

2. Placethesheetofpaperoverthemagnet.

3. Tracetheoutlineofthemagnet,showingthenorthandsouthpoles.

4. Evenlysprinkleironfilingsoverthepaper.Distributethefilingssotheshapeofthepatternonallsidesofthemagnet

isdelineatedbytheironfilings.

5. Repeatwiththefollowingcases.

6. Theironfilingscanbeeasilypouredbackintothecontainer.Iftheycomeintodirectcontactwiththemagnet,itis

muchhardertocleanup.

–Twonorthpolesfacingeachother

–Anorthandasouthpolefacingeachother

–Ahorseshoemagnet

–Anyothershape—yourchoice

ExpectedResults

Theelectricfieldsurroundingabarmagnetfollowslinesthatgofromthenorthpoletothesouthpole,asshowninFigure

111-1.

Withanorthpoledirectlyoppositeasouthpole,thelinesofforcearedirectedfromthenorthpoletothesouthpole,as

showninFigure111-2.

Withtwonorthpolesfacingeachother,theelectricfieldisdirectedawayfromeachofthepoles.Linesofforcecanbe

seendirectedperpendiculartoeachofthetwomagnets,asshowninFigure111-3.

378

Figure111-1Barmagnet.

Figure111-2Northpoleoppositesouthpole.

WhyItWorks

Themagneticfieldcausesferromagneticmaterials,suchasironfilings,toalignwiththefieldlines.

OtherThingstoTry

Ahighertechapproachwouldbetouseamagneticfieldsensortomapouttheshapeofthesemagneticfields.

Figure111-3Northpoleoppositeanothernorthpole.

ThePoint

Magneticfieldsshowtheforceamagnetwouldexertonthenorthpoleofanothermagnet.Magneticfieldspointfromnorth

tosouth.Magneticfieldspointawayfromnorthpoles(oppositesrepel)andtowardsouthpoles(likesattract).

379

Project112

Whathappenstoacurrent-carryingwireinamagneticfield?

TheIdea

Theheartandsoulofanelectricalmotorismovementcreatedwhenmagnetsrepeleachother.ThediscoverybyMichael

Faradaythataforceisproducedwhencurrentflowsthroughamagneticfieldwasagroundbreakingdiscovery,whichpaved

thewayfortheeventualdevelopmentoftheelectricmotor.

WhatYouNeed

powerfulhorseshoemagnet

DCvoltagesource,suchasanadjustablepowersupply,amotorcyclebattery,oracarbattery

about1meter(afewfeet)ofinsulatedwire

ringstandwithclampstopositionthewire

Method

1. Setthehorseshoemagnetonthetable.

2. Positionthewiremidwaybetweenthenorthandsouthpolesofthemagnet.Thewireshouldrunperpendiculartothe

twoendsofthemagnetanditshouldbeabletomove.

3. Attachoneendofthewiretothenegativeterminalofthepowersupply,asshowninFigure112-1.

4. Brieflytouchtheotherendofthewiretothepositiveterminalandobservethewirepassingbetweenthepolesofthe

magnet.Ifyouareusinganadjustablepowersupply,startwithalower-currentoutputsettingandslowlyincreaseit

until thewireresponds.Becausethere isnoresistancebesidesthe littleresistancethewireoffers,ahighcurrent

mayflowthatmaycauseafuseorcircuitbreakertoblow.

ExpectedResults

Withcurrentflowinginthewire,themagnetpushesthewireawayfromthemagnet.

WhyItWorks

Aforceisexertedonamovingcharge(orcurrent)inawiremovingperpendiculartoamagneticfield.

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Figure112-1Forcebetweentwocurrent-carryingwires.

OtherThingstoTry

Repeatthiswithatightcoilofthewireinthemagneticfield.Comparewiththeresponseofanuncoiledwire.

ThePoint

Amagneticfieldexertsaforceonacurrent-carryingwire.Thedirectionofthatforcedependsonthedirectionofcurrentflow

andtheorientationofthemagneticfieldaccordingtotheright-handrule.

381

Project113

Ano-frillsmotor.

TheIdea

Inthisprojectyouwillbuildaverybasicelectricmotor.Thisprojecthasbeenbrokendownintoanumberofstepsforclarity,

buttheoveralldeviceissimple.It’slikeassemblingabarbequegrill—thefirsttimeyoudoitmaytakealittlelonger,butonce

yougettheoverallidea,itgetseasiereachtime.Ittakesjustafewminutestobuild,butitcankeeprunninguntilthebattery

runsout.

WhatYouNeed

CorDcellbattery

ceramicdiscmagnet

1meterofenamel-coated(thin)22AmericanWireGauge(AWG)wire. It ismucheasiertoworkwithredorgreen

coatedenamel,ratherthanclear-coated

2paperclipsorafewinchesofatleast20AWGwire

Figure113-1Partstoassemblea“no-frills”motor.

electricaltape

optional:batteryholder,Styrofoamcup

Method

1. Windabout25–30turnsofthe22gaugewirearoundacylindricalcoilform,suchasaballpointpenorasmallAAA

battery.

2. Leaveafewofinchesofwirefreeateachend.

3. Pull thecoil off the formyouwound itaround.Becarefulandhold thewire, so it doesn’t springoutof shape (it

doesn’thavetobeperfecttowork).

4. Weave each of the ends of the wire around the coil a few times to hold the coil together. This becomes the

armatureofthemotor.Ifyouprefer,youcanalsousetapetohelpkeepthecoiltogether.

5. Theendsofthewireshouldbeplacedinastraightlinetomakeagoodaxle.Itcanhelpifyoudoubleback,sothe

endsectionsconsistofmorethanonethicknessofwire.Italsohelpstooverwraptheendswiththelastsegmentof

wireortape.

382

6. Usingautilityknife, removethe insulationfromthetophalfofthe22gaugewireatbothends.Youcanalsouse

sandpapertodothis.Ifthewireiscoatedwithacoloredlayer,youcanseewhentheinsulationhasbeenremoved.If

thewireisclear-coated,youmustbemorecarefulandkeeptrackofwhereyouareremovingtheinsulation.Donot

removetheinsulationfromthebottomhalfofthewire.

7. Whenyoufinish,thesidewiththeinsulationremovedmustremainfacinguponbothends.

8. Makeanarmaturesupportbyfirstformingthepaperclipsintoaloop.Ifyouareusingwire,removeinsulationfrom

eachoftwo1½-inchsectionsofwireandformasmallcircularloopabout1millimeterindiameterinthecenterof

eachwire.Anailcanserveasagoodformtowraptheloop.

9. Bendthewirestoformashapelikeawishbonewiththewireendsseparatedbyafewmillimeters.

10. Thetwoendsofthecoilsshouldeasilyfitintothearmaturesupportsandshouldbeabletoturnfreely.

11. Securethearmaturesupportwirestothebatteryholderwithtape.

12. Establishelectricalcontactbetweenthearmaturesupportsandthepositiveandnegative terminalsof thebattery

holder.Youmayneedtousejumperwirestodothis.

13. Insert the endsof thearmature (coil) into the holes of thearmature supports. Thearmature supports should be

spacedfarenoughapartsothecoilissupportedatbothends.

14. Tapethebatterytothetopofthecuporinsertthebatteryintotheholder.

15. Attachthemagnettothetopofthebatteryholderjustunderneaththecoil.UsetapeorVelcrotodothis.Makesure

thecoilcanstillspineasilyandthatitisjustabovethemagnet.Itmaybenecessarytoraiseorlowerthearmature

supportstoattainthecorrectheightabovethemagnet.

16. Spinthearmaturegentlytogetthemotorstarted.Ifitdoesn’tstartspinning,tryspinningitintheotherdirection.It

willonlyspininonedirection.

Thismaysoundlikealotofsteps,butitisverysimple,asshownbyFigure113-2,whichshowswhatthismotorlookslike

whenitisallassembled.

Figure113-2BasicDCmotor.

ExpectedResults

Themotorshouldkeepturninginonedirection.

If itdoesnotrun,checkallelectricalconnections.Besureonesupporttouchesthenegativeendofthebatteryandthe

othersupporttouchesthepositiveend.Besurethearmaturecanspinfreely.It isessentialthattheinsulationberemoved

fromonlyone-halfoftheturnsandtheuninsulatedsideofthewireisfacingthesamedirection.

WhyItWorks

383

Thebasicconceptofamotoristherepulsionoftwomagneticfields,resultinginarepetitiveturningmotion.Onemagnetisa

permanentmagnet.Theotherisanelectromagnetformedbyacoilofwirethroughwhichanelectricalcurrentisflowing.The

trickisonlytohavethemagneticfieldsrepel,butnotattract.Ifwehadtakentheinsulationoffthetopandbottomsidesof

theenamel-coatedwireused for thecoil, themotorwouldgonomore thanone-half turn,and thenstopas thecoil and

permanentmagnetattractedeachother.By leavingthe insulationonthebottomhalvesof thecoilwires,nocurrent flows

throughthecircuitatatimewhenthemagnetswouldattract.Inourcase,themomentumofthecoilkeepsitrotatinguntilthe

uninsulatedwiresemerge just in time for thepermanentmagnet to repel thecoiland rotate throughanothercycle.Other

motordesignshavewhatiscalledasplitcommutator,whichgoesonestepbetterbychangingthedirectionofthecurrent

flowingthroughthewire,sothemagnetsarealwaysrepulsive.

OtherThingstoTry

Double the spinning power by constructing a split-ring commutator. Try this bymaking the followingmodifications to the

simplemotorconceptpreviouslydescribed:

1. Insulatethetophalfoftheloopofonearmaturesupportandinsulatethebottomhalfoftheotherarmatureloop.

2. Startingwith insulatedenamel-coatedendsofthe22gaugewire, removethe insulationfromthetopononeside

andthebottomontheotherside.

3. Onceyoustartthemotor,thecontactshavebeensetuptomakesurecurrentflowsthroughthecoilatatimeandin

adirectionthatresultsinacontinuousrepulsiveforce.

ThePoint

Amotorconsistsofthefollowingfundamentalcomponentsillustratedinthisproject:Theseincludeapermanentmagnetand

anelectromagnetthatreceivesDCcurrentonlyduringthoseportionsofitscyclewhenitwillberepelledbythepermanent

magnet.

384

Project114

Magneticaccelerator.

TheIdea

This is a simple experiment with a very unexpected outcome. A steel ball is rolling in a track drawn by amagnet. The

seeminglygentleforceproducesapowerfulaccelerationthatpropelstheballathighvelocity.Theresultsarequiteamazing

andprovideaninterestinginsightintothenatureoflinearmomentum,aswellasmagneticfields.

WhatYouNeed

4stainlesssteelballs

1neodeumcylindricalmagnet

tracktoguidethesteelballs(agroovedmountingbracketforcurtainsworkswell,andithastheaddedadvantageof

providingahandyend“bumper”)

Method

1. Placethesteelballsinthetrack.

2. Groupthreeballstogether.

3. Rollthefourthballtowardtheotherthree.

4. Noticewhathappens.(Thisisnotthesurprisingpart,butitestablishesabaselineofexpectation.)

5. Placethreeballsonthetrack.Then,placetheneodymiummagnettotherightofthethreeballs.

6. RollthefourthballfromtherightsideofthemagnetwithaboutthesamespeedastheballinNumber3.

ExpectedResults

Withoutthemagnet,theincomingsteelballstopsandknocksoutanotherball.Thedislodgedballcontinueswiththesame

velocityoftheincomingball.Thisisthefamiliarcaseofconservationofmomentumduringanelasticcollision,asshownin

Figure114-1.

Withthemagnetinplace,asingleballisalsoknockedout,asshowninFigure114-2.However,theballthatisknockedout

surprisinglymovesatturbospeed—muchfasterthanthevelocityoftheincomingball.Themagnetincreasesthevelocityof

the incomingball.Thismuchhighermomentumat the last instant is imparted to theoutgoingball,whichshootsoffata

surprisinglyhigherspeed.

Figure114-1Theincomingballdislodgesoneballthatexitswiththesamevelocityastheincomingball.

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Figure114-2Themagnetdramaticallyincreasesthemomentumoftheballatthelastminute.

WhyItWorks

Inbothcases, linearmomentumisconserved.Withthemagnet, the incomingball isacceleratedandachievesaveryhigh

instantaneousvelocityjustbeforeithitsthemagnet.Conservationofmomentumrequiresthattheoutgoingballmovesatthat

samehighvelocity.

Linearmomentum is always conserved if no force is doing work. In physics, work is force applied over a distance. A

principleofphysicscalledthework-energytheoremstatesthatifaforceisexertedoveradistance,thekineticenergyofan

object(and,asaresult,itsvelocity)changes.Inthiscase,amagneticforceisdoingwork,whichacceleratesthesteelball.

Becausethemagneticforceincreasesastheballapproachesthemagnet,thespeedpicksupatanevengreaterratethan

aconstantforce.

OtherThingstoTry

Repeatwithothercombinationsofballsoneithersideofthemagnet.

ThePoint

Linearmomentumisthesamebeforeandafteracollision.Becausethesteelballisacceleratedrapidlybythemagnet,the

velocityoftheball(anditsmomentum)isveryhighjustbeforethecollision.Conservationoflinearmomentumrequiresthe

velocityoftheballafterthecollisionalsobeveryhigh.

386

Project115

Alternatingcurrent.

TheIdea

Inthissection,youexploresomeofthebasicaspectsofACcurrent.

Theelectricalpowerweget fromabattery iscalleddirectcurrent (DC).A9-voltbatteryproducesavoltageof9volts,

whichdoesn’tchangeuntilthebatteryisusedup.Theelectricitywegetdeliveredfromtheelectricalpowercompanyfrom

thewallsocketisAC(alternatingcurrent).Thisisdifferentthanabatterybecausethevoltageandcurrentcomingfromour

wallsocketsiscontinuouslychanging.Thevoltagereversesdirection60timeseverysecondinNorthAmerica(and50times

eachsecondinmostofEuropeandmuchofAsia).

ACishowelectricityisdistributedthroughouttheworld’spowergrid.SometimesDCneedstobeconvertedtoAC,suchas

solarelectricpanelsusedtoprovidepowerforanelectricalutility.SometimeACneedstobechangedtoDCatadifferent

voltage,suchasisdoneincellphonebatterychargers.

WhatYouNeed

Displayinganalternatingcurrent

waveformgeneratorandanoscilloscope

connectorfortheoscilloscope(consistingofaBNCconnectorwithtwowireleadsattached)

diode

alternative: a source of sound, amicrophone, and a computer-based, sound-card oscilloscope.CAUTION: Sound

cardoscilloscopescanhandleonlylow-voltageinputs,suchasfrommicrophones.Attemptingtouseasound-card

oscilloscopeforlargerelectricalsignalmaydamageyoursoundcard.Ahigh-impedancecircuitthatwillenableusing

a sound-card oscilloscope for higher voltages can be found at

www.geocities.com/~uWezi/electronics/projects/soundcard_osci.html.

Buildingatransformer

2-footlengthofinsulatedwire

4-footlengthofinsulatedwire

largeironnail

ACpowersupply,waveformgenerator,orkeyboardoutput

2ACvoltmeters(ormultimetersconfiguredasanACvoltmeter)

Method

Whata60-cycleACsignalsoundslike

1. IfyouhaveanadjustableACpowersupply,attachoneoftheterminalsofthespeakertothepositiveterminalofthe

ACpowersupplyandtheotherspeakerterminaltothenegativeterminalofthepowersupply.

2. Slowlyturnupthevoltageandyouwillstarttohearthecharacteristic60-cyclehumcomingfromthespeaker.This

maybeafamiliarsoundtorockmusiciansworkingwithpreownedPAsystems,whichoftenleaksintoaudiosystems.

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Whatan60-cycleACsignallookslike

1. ConnectthepositiveandnegativeterminalsoftheACpowersupplytoa1000ohmresistor.

2. Attach the two wire leads of the oscilloscope input to the two ends of the resistor. (Do not use a PC-based

oscilloscope,whichweusedinotherexperiments,unlessyouhaveaspecialcircuittoadapttheACsignalforthis

purpose.)

3. TurnontheACpowersupplywithjustenoughvoltagetoproduceadisplayontheoscilloscope.

4. Adjust the amplitude, time sweep, and, if necessary, trigger setting to display the AC signal on the oscilloscope

screen.Figure115-1showshowtheelectricalcomponentsareconnectedtomakethismeasurement. (Thediode

usedinthenextsetofstepsisshownconnected.)

Whatadiodedoestoanalternatingcurrent

1. Removeoneoftheconnectionstothepowersupply.

2. Attachadiodeinthecircuitgoingfromthepowersupplythroughtheresistor.

3. TurnontheACpowersupply.

4. Reattachtheleadsfromtheoscilloscopetotheendsoftheresistor.

5. DisplaytheACsignalontheoscilloscopescreen.

Figure115-1

6. TurndowntheACpowersupply.

7. Removethediode.Reversethedirectionoftheleadandreattachthediodeinthecircuit.

8. WiththeACpowersupplyturnedon,observehowthesignalchanges.

Buildingatransformer

1. Windthe2-footsectionofwirearoundthenail.Leaveapproximately6-inchlengthsofwireateachend,withabout

¾oftheinsulationremovedfromtheendsofthewire.Keeptrackofhowmanyturnsyouapply.

2. Dothesamewiththe4-footsectionofwire.Thereshouldbetwiceasmanyturnsonthissection.

3. AttachthepositiveandnegativeofanACpowersupplytothetwoleadsofthe2-footsectionofwire.(Wecancall

thistheprimarycoil.)

4. AttachthetwoendsofanACvoltmetertothepointsofcontactbetweenthepowersupplyandthe2-footsectionof

thetransformerwire.

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5. AttachtheotherACvoltmetertothetwoleadsofthe4-footsectionofwire.Whatdoyouread?

6. IfyouhaveaDCpowersupplyavailable,applyasimilarvoltagetotheprimarywindings.Howisthevoltageofthe

secondaryaffected?

ExpectedResults

A60-cycleACsignalisdisplayedonanoscilloscopewithafullwavelengthrepeatingevery0.017seconds.AnACsignalhas

theformshowninFigure115-2.

Insertingthediodeinthecircuitresultsinonlyone-halfofthewaveformflowinginthecircuit.Thismeansonlythepositive

(ornegative)halfofthecycleisdisplayed,asshowninFigure115-3foradiodeplacedinonedirection,orasinFigure115-4

foradiodeplacedintheotherdirection.

Figure115-2Alternatingcurrentwaveform.

Figure115-3Alternatingcurrentwithadiode.

Figure115-4Alternatingcurrentwithadiodefacingtheotherway.

WhyItWorks

Alternatingcurrentisconstantlychangingdirection.

Adiodeisadevicethatpassesthecurrentinonlyonedirection.

A transformerchanges theACvoltageofan incomingsignalbasedon the ratioof turnsbetween the inputandoutput

sidesofatransformer.AtransformeronlyletsACcurrentthrough,butitwillnotpassDCcurrent.

Theratiooftheprimary(in)tothesecondary(out)voltageofatransformeristheratiooftheturnsofthesecondarytothe

primary.Thisisgivenbytheequation whereVrepresentsthevoltage,Nthenumberofwindings,p

theprimary,andsthesecondarywindings.

OtherThingstoTry

Ifyoudon’thaveastand-aloneoscilloscope,herearesomeotheroptions:

1. Buildanadapterforthesoundcardoscilloscope.

2. Useanaudibletone,suchasfromanelectronicsynthesizerkeyboard,toproduceasignalthatiscompatiblewitha

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soundcardoscilloscope.

3. YoucanalsogenerateanACsignalusingamagnetsuspendedbyaspringoveracoil.Thesignalcanbemonitored

byasoundcardoscilloscopeorPASCOvoltagesensor,andtheeffectsofthediodescanbestudied.

ThePoint

Alternatingcurrentconsistsofa flowofelectronscontinuously reversingdirection.Thevoltageofacommon formofAC

followstherisingandfallingpatternofasinewave.

390

Project116

Thediode.Anelectronicone-wayvalve.

TheIdea

Adiodeisanelectronicdevicethatletscurrentflowinonlyonedirection.Diodesarefoundinelectroniccircuitsandformthe

basisformorecomplicateddevices,suchastransistorsandintegratedcircuits.LEDs(light-emittingdiodes)andsolarcells

arediodes.

Unliketheresistorswestudiedinpreviousexperiments,diodesdonotfollowOhm’slaw.Theyarecallednonlineardevices,

whichgivesthempropertiesthatareusefulinawidevarietyofelectronicapplications.

WhatYouNeed

diode

DCpowersupply

voltmeter

ammeter

jumperwires

Method

1. Setupthecircuit,asshowninFigure116-1.Thisconsistsofthepositiveterminalofthepowersupplyconnectedto

thepositiveendofthediode(identifiedbythelongerofthetwoleads).Theammeterisconnectedinserieswiththe

diodeand,together,theyareattachedtothepowersupply.Thevoltmeterisconnectedtothetwoterminalsofthe

diode.

2. Startwiththepowersupplyatthelowestlevelandmakesurethevoltageandcurrentmetersreadzero.

3. Very slowly, walk the voltage up, taking current and voltage readings at each step. Continue until the current

suddenlygoesupsignificantlyhigherthanpreviouslevels.Donotallowtoomuchcurrenttofloworthediodecanbe

damaged.

ExpectedResults

Therelationshipbetweenvoltageandcurrentisnotlinear.

Asthevoltageincreases,athresholdisreachedwhereasmallincreaseinvoltageresultsinahugeincreaseincurrent.

391

Figure116-1Diodetestcircuit.

Thisrelationshipbetweencurrentandvoltageisexponential.

WhyItWorks

Thecurrentthatpassesthroughadiodeisrelatedtothevoltageappliedacrossitbythediodeequation:

I=IoeqV/kT

whereI isthecurrentandV isthevoltage(qandkareconstants,T isthediodetemperature,andIo isapropertyof the

diode).

Thisequationshowsthatthecurrentincreasesexponentiallyasthevoltageisincreased.Atfirstthechangeisslow.But

afterabout0.7V,thediodeofferslittleresistancetotheflowofcurrent.

OtherThingstoTry

Current-voltagecharacteristics

Plotthecurrentversusvoltageonalinearplot.Itsshapeisexponentialwitha“knee”around0.7Vdefiningaregionwherea

small increaseinvoltagecausesavery largeincreaseincurrent. Ifyouplotthelogofthecurrentversusthevoltage,you

shouldgetastraightlineatleastoveramajorpartofthedatarange.Ifvoltageisalogarithmicfunctionofcurrent,currentis

anexponentialfunctionofvoltage.Plottingthisconfirmsthenonlinearbehaviorofthediodecharacteristic.

Voltageinthereversedirection

Whathappens ifyouswapthetwo leadsofthediode?Thisappliesavoltage intheoppositedirectionas intheprevious

case.Asaone-wayvalve,thediodedoesnotallowanymeasurablecurrenttoflowinthereversedirection.Ifyoutrytoforce

theissueandcontinuetoincreasethevoltage(goingthewrongway),youmay(dependingonthediode)reachacondition

calledthebreakdownvoltage.Whenthishappens,theoppositiontothecurrentflowbreaksdownandthediodeallowsthe

currenttoflow.Inmanydiodes,thisisareversiblecondition,whichcanbeusedtoestablishasetvoltagelevelinacircuit.

Goingintobreakdownmaydamagesomediodes,sobecarefulifyoutrytomeasurethisinyourcircuit.

ThePoint

392

Adiodeisanonlineardevice.Asmallincreaseinvoltageproducesalargeincreaseincurrent,whichgrowsexponentiallywith

voltage.

393

Section10

TheEarth

Project117

MeasuringtheEarth’smagneticfield.

TheIdea

TheEarthhasamagneticfieldthatgoesfromtheSouthPoletotheNorthPole.ThemagneticSouthPoleisactuallycloseto

the geographic North Pole. We can measure how strong the horizontal component of the Earth’s magnetic field is by

comparingitseffecttothatofamagneticfieldproducedbythecurrentflowinginacoilofwire.

WhatYouNeed

insulatedwireseveralmetersinlength

compass,preferablyonemountedonalow-frictionpivot

ruler

protractor

cylindricalshapetowrapthecoil (Thediameteroftheshapedependsonthe lengthofthecompassneedle.The

diameterofthecoilneedstobelargerthanthelengthofthecompassneedle.)

ringstandorothersupporttoholdthecoilofwire

DCpowersupplycapableofcurrentintherangeof1.0amporhigher

DC-ammeteroramultimeterconfiguredasanammeterinthe0–10Arange

roomwithnonferroustablesandfreeofstraymagneticfields

Method

1.Setupthecompass.Makesureitisfree-spinningandpointingtothenorth.Metaldeskscontainingironorsteelmay

interferewiththis.Also,motorsorloudspeakersmayhavesignificantmagneticfieldsthatcouldaffecttheoutcomeof

thismeasurement.

2. Form a coil of 15 turns using the cylindrical shape to form the coil. (For a small hand-held compass, a 1½ inch

diameterpipeisagoodform.Forthepivottypecompass,asoupcanorcoffeecanismoreappropriate.)Afterthe

coilisformed,withdrawtheobjectusedtowindthecoil.Leavesomewireatthestartandendofthecoiltoallowitto

beconnectedintoacircuit.

3.Supportthecoilusingaringstandorothersupport.Thecoilisorientedverticallywiththeplaneofthecoilfacingeast

andwest.Thecompassshouldbecontainedinsidetheplaneofthecoil,asshowninFigure117-1.Atopviewofthis

isshowninFigure117-2forclarity.Noticetheendsofthecompasspointstotheturnsofthecoil.

4.MakesuretheDCpowersupplyisturnedoffandtheammeterissettoreadcurrentsintherangeof1–10amps.

5.Afterstrippingtheinsulationfromtheendsofthecoil,attachoneendtothepositiveterminaloftheammeterandthe

otherendtothenegativeterminaloftheDCpowersupply.Youcanusejumperwiresorattachthecoildirectly.Refer

toFigures117-1and117-2fortheappropriateconnections.

6.CompletetheelectricalcircuitbyconnectingthenegativeterminaloftheammetertothepositiveterminaloftheDC

powersupply.

7.Placetheprotractorsothezerodegreeline insalignedwiththedirectionthecompassexposedonlytotheEarth’s

magneticfield.

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Figure117-1SetupformeasuringtheEarth’smagneticfield(sideview).

395

Figure117-2SetupformeasuringtheEarth’smagneticfield(topview).

8.Slowlyandcarefully turnon theDCpowersupply. Increase thecurrent readingon theammeteruntil thecompass

needledeflects45degreesfromitsstartingposition.

9.Atthispoint,thehorizontalcomponentoftheEarth’smagneticfieldisbalancedbyandequaltothemagneticfieldof

thecoil.

TheEarth’smagneticfieldis:

(1.26×10−6isthesameas0.0000126andyoucanmultiplyinchesby0.00254togetmeters.)

ExpectedResults

TheEarth’smagneticfieldvarieswithlocation,butitisintheballparkofabout5microTeslasor5μTor5×10−7T.Thefollowingtablesummarizestheresultsfordifferent latitudes,and it includesthescientificnotationanddecimalformsthat

396

areequivalent.

WhyItWorks

Themagneticfieldofthecoil isperpendiculartotheplaneofthecoil. Inthisexperiment, themagneticfieldofthecoil is

perpendiculartothehorizontalcomponentofthemagneticfieldoftheEarth.Whenthecoil’smagneticfieldjustequalsthe

horizontalcomponentof theEarth’smagnetic field, the resultantpointsata45-degreeanglebetweenthe two.When this

occurs,themagneticfieldoftheEarthisgivenbythatofthecoilaccordingtotheequation:

whereBisthecoil’smagneticfieldinTeslas

Nisthenumberofturnsinthecoil

μo isameasureofhowstrongamagneticfield isproducedbyagivencurrent,calledthepermeabilityoffreespace,and

equals1.26×10−6TeslasIisthecurrentinamps

Ristheradiusofthecoilinmeters.

Asanexample:A15-turncoil that is2 inchesindiameter(or0.051meters)requiresacurrentof0.28ampstoturnthe

compass45degrees.

Themagneticfieldis:

B=(15turns×1.26×10−6T-m/A×0.28A)/(2×0.051m)=0.00000052Tor5.2×10−5TThisisintheballparkoftheexpectedrangefortheEarth’smagneticfieldformiddlelatitudes.

OtherThingstoTry

The previously measured value is the horizontal component of the Earth’s magnetic field. Near the equator, the Earth’s

magnetic field isall horizontal.Asyouapproach thepoles, thedirectionof themagnetic fieldwith respect to theEarth’s

surface increases.Theangle the fieldmakeswith theEarth’ssurfacecanbemeasuredusingacompass that is free to

rotateintheverticalplane.Thetotalfield(ortheoverallfieldstrengthvector)atthatlocationcanbedeterminedfrom:

totalfield(Teslas)=horizontalcomponent(Teslas)/cosine(angletohorizontal)

Aswithmanyexperiments,itiscomfortingtoknowthattheeffectweintendtomeasureis,infact,whatourexperimental

resultsaregivingus.Onewaytoincreaseconfidenceinourresultsistorepeatitunderdifferentconditionandverifywehave

thesameoutcome.Accordingtoourmodel,itshouldnotmatterhowmanycoilswehave.Repeatingthemeasurementtosee

howmuchcurrentisneededtoturnthecompass45degreesusing5,10,or20coilsshouldgiveaconsistentresultasthe

measurementdescribedaboutusing15coils.

ThePoint

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ThemagneticfieldoftheEarthcanbemeasuredbybalancingitwithaknownmagneticfield.Ifthatmagneticfieldisatright

anglestothehorizontalcomponentoftheEarth’smagneticfield,thecompasswillpointinanewdirectionthatis45degrees

fromtheoriginalposition.Awayfromtheequator, theEarth’smagneticfield isatanangletothehorizontal,whichcanbe

measured.Theoverallmagneticfieldwillbeslightlyhigherthanthehorizontalcomponent.

398

Project118

WeighingtheEarth.

TheIdea

ShortlyafterSputnikwaslaunchedbytheformerUSSR,PresidentDwightDavidEisenhower,askedhisgeneralstotellhim,

based on its orbit, howmassive the satellite was. Unfortunately, they were unable to provide the U.S. president with the

informationherequested.However,theywouldhavebeenable,instead,totellhimthemassoftheEarth(whichEisenhower

wasn’tconcernedabout). In thisproject, youuseadifferentsatellite—themoon—todetermine themassof theEarth.You

alsoexplorehowthescientistCavendishperformedsomepainstakingcalculationsofgravitationalattractionandwasable

toaccomplishthesamething.

WhatYouNeed

moon

calendar

Method

1. DeterminehowlongittakesforthemoontocircletheEarth.

2. Acalendarcangiveareasonableresult.Amoreaccuratevalueisthesiderealperiod,whichindicatesonlythetime

ittakesforthemoontocircletheEarth,withoutconsiderationforhowlongittakestoreturntoaparticularphase.

This can beobtained froma sidereal table or by subtracting2.2 days from the valueobtained by observing the

numberofdaysfromonefullmoontoanother.

3. Calculatethevelocityofthemooninitsorbitbasedonitsaverageradius,r,of384,400kilometers(3.844×108m).Youcandothisusingtheequation:

1. CalculatethemassoftheEarthusingtheequation

whereGistheconstantofUniversalGravitation=6.67×10−11m3/kgs2

ExpectedResults

Usingthefollowingvalues:

T=27.322days=2,360,621seconds

v=2πr/T=1,023meters/secondr=3.844×108m

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Thisiswithin1percentoftheacceptedvalueforthemassoftheEarthof5.97×1024kilograms.

WhyItWorks

Newton’s law of universal gravitation states there is an attractive force between any two masses in the universe. The

attractiveforceisrelatedtohowmassivetheobjectsareandhowfaraparttheyarefromeachother.Thegravitationalforce

is linkedtothemassanddistancebyaconstant,“bigG,”calledtheuniversalgravitationconstant.Since thegravitational

forceistheforcethatprovidesthecentripetalforcethatkeepsasatelliteinorbit,wecansolveforthemassoftheEarthif

weknowtheothervariablesintheequation.Similarly,knowingthatthegravitationalforceequalstheweightofanobject,we

cansolveforthemassoftheEarth.

OtherThingstoTry

Cavendish’s famousexperiment is oneof our “wish-list” experiments that canbe used to determine the bigGand, asa

result,themassoftheEarth.GravitationalforcebetweentwomassescanbemeasuredusinganapparatusshowninFigures

118-1and118-2.Therelativelysmallforceisdetectedbymeasuringthetorsionitproducesinathinfilamentbetweenthe

masses.

ThePoint

Themassofabodythatasatelliterotatesaroundcanbedeterminedbytheorbitalperiodofthatsatellite.Akeycomponent

oftheforceistheuniversalgravitationalconstant,G.ByknowingG,itispossibletodeterminethemassoftheEarth,using

eithertheweightofobjectsontheEarth’ssurfaceortheorbitalperiodofsatellitescirclingaroundtheEarth.

Figure118-1Cavendishapparatus.

400

Figure118-2TopviewofmassesintheCavendishapparatus.

401

Section11

TheTwentiethCentury

Project119

Whatisthesizeofaphoton?

TheIdea

One of the pivotal discoveries of the twentieth century was the recognition that light ismade of photons, which can be

thoughtofasminuteparticlesof light.Lightbehaves inmanyways likeawave,but italsobehaves inmanywaysas if it

consistedofparticles.Justhowbig(orsmall)aretheseparticlesoflight?

WhatYouNeed

severalLEDs(light-emittingdiodes)ofknownwavelength

variablepowersupply

jumperwires

voltmeter(ormultimeterconfiguredasamultimeter)

darkroom

Method

1. Attach the positive end of the voltmeter to the positive end of the power supply, and the negative end of the

voltmetertothenegativeendofthepowersupply.

2. Adjustthepowersupplytogiveareadingofzerovolts.

3. SelectanLED.UsejumperwirestoconnectthepositivesideofthepowersupplytothepositiveterminaloftheLED.

(ThepositiveterminaloftheLEDisthelongerone.)

4. ConnectthenegativesideofthepowersupplytotheLED.

5. Darkentheroom.

6. SlowlyincreasethevoltagefromthepowersupplyuntiltheLEDjustbeginstogiveofflight.Forvisiblelight,thiswill

bebetween1.2voltsand2.5volts.

7. Writedownthevoltagethatresultsinlightjustbeingproduced.

8. RepeatthisprocessforalltheLEDsyouhave.

9. Makeagraphofvoltageversusfrequency.

TheschematicforthisexperimentisshowninFigure119-1.

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Figure119-1CircuittomeasureLEDturn-onvoltage.

ExpectedResults

Thehigher thefrequency, thehigher thevoltageneededto turnon theLED.Therelationship is linear,asshown inFigure

119-2.

WhyItWorks

Accordingtoquantumtheory,theenergyofaphotondependsonitsfrequency.Higherfrequencylight(orlightclosertothe

bluesideof the visible spectrum)hasmoreenergy. Lower frequency light (closer to the redside) has lessenergy. Fora

photonofagivenfrequency,f,orcolor,theenergyisgivenbyhf,wherehiscalledPlanck’sconstant.

Figure119-2LEDvoltageversusfrequency.

403

OtherThingstoTry

TheamountofenergyneededtoturnonanLEDisgivenbyqV,whereqisthechargeofanelectron=1.6×10−19CandVis theappliedvoltage.Fromtheslopeof thegraph,youcanestimatePlanck’sconstant (fromtheslopeof thepreviously

plottedequation, v= (h/q)f).Planck’sconstantcanbedeterminedbydividing theslopeof thegraphby thechargeofan

electron.TheacceptedvalueforPlanck’sconstantis6.63×10−34J-s.TheslopeofthegraphinFigure119-2isabout7×10−34J-s,whichprovidesareasonableorderofmagnitudeestimateofPlanck’sconstant.

Sohowsmallisaphoton?Let’stakea60Wlight.Thismeansthatatabout5percentefficiency,thereareabout3Joules

ofenergycomingfromthebulbeverysecond.AccordingtoPlanck’sconstantthismeansthateverysecond3J/6.63×10−34

J-s = 4.5× 1033 photons are coming from the light bulb. This incredibly large number of photons gives an idea of theextremelysmallsizeofthephoton.

ThePoint

Theturn-onvoltageforanLEDgivesanindicationofhowmuchenergyiscontainedinasinglephoton.Photonswithhigher

frequency(shorterwavelength)havemoreenergythanphotonswithlowerfrequency.

404

Project120

HowisahydrogenatomliketheNewJerseyTurnpike?Seeingtheenergylevelsofthe

Bohratom.

TheIdea

In this experiment, you look at the colors of the light that the atoms of a particular element give off when excited by

electricity.Thisisthesametypeofdatathatledsomeofthegreatestscientificmindsofthetwentiethcenturytodevelop

theconceptoftheatom.Thepatternsofthosecolorsgiveusinsightintothemysteriesofthestructureoftheatom.Likethe

NewJerseyTurnpike,theelectronsinthevariousenergylevelsofthehydrogenatomcanexitonlyincertainspecificways.

WhatYouNeed

diffractiongrating

tubeofhydrogen

high-voltagepowersupplytoexcitethehydrogen

Method

1. Insert thehydrogen tube into thehigh-voltagepowersupply.Makesure thegoodelectricalcontact isestablished

betweentheelectrodesofthehydrogentubeandthepowersupply.

2. CAUTION:Do not touch the electrical contacts of the high-voltage power supply once it is activated. Follow all

manufacturer’sinstructionsforsafeuseofthisequipment.

3. Darkentheroom.

4. Turnonthepowersupplyandobserveaviolet-blueglowinthetube.

5. Holdadiffractiongratingwiththescribedlinesparalleltothetubeinfrontofyoureyes,asindicatedinFigure120-1.

6. Observetheimageoftheglowinghydrogentubebrokendownbythediffractiongrating.Ifyouhaveaspectrometer,

observe the light from the hydrogen tube and identify the positions of each of the lines you see. Look for the

transmittedlighttotheleftandrightofthecentralimagefromwhichtheglowinghydrogentubeislocated.Youmay

needtouseyourperipheralvisiontoseetheentireeffect.

ExpectedResults

Thelighttransmittedthroughthediffractiongratingisnotacontinuousrainbow.

Thelightisbrokendownintoafewbrightverticallines.

ThedetailsofthelinesyouseearesummarizedinTable120-1.

WhyItWorks

OntheNewJerseyTurnpike,ifyougetonatExit6andgotoExit7,youpaya$0.80toll.IfyougofromExit6toExit8,you

pay$1.20.Inahydrogenatom,ifanelectrongoesfromthethirdenergyleveltothesecondenergylevel,onlyredphotons

(withawavelengthof656.3nanometers)arereleased.But, ifanelectrongoesfromthefourthenergyleveltothesecond

energylevel,onlyblue-greenphotons(withawavelengthof486.1nm)areemitted.

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Figure120-1Measuringthespectrumofthehydrogenatom.

OntheNewJerseyTurnpike,nothingisbetweenExit6and7,andyouneverhavetopayatollbetween$1.20and0.80.

Thehydrogenatomdoesnotproduceaphotonwhosecolorisbetweenredandblue-green.

Einstein’sinterpretationofthephotoelectriceffectleadsustotheconclusionthatphotonshaveacertainspecificenergy

basedontheirfrequency.NielsBohrdevelopedamodelofthehydrogenatombasedontheideathattheelectronsarefound

incertainspecificenergylevels,butnotinbetween.Aparticularchangeinenergylevelsresultsinaphotonofaparticular

color.

Whenviewedthroughadiffractiongrating,thelightfromtheexcitedhydrogenatomsdoesnotresult inafullrainbow.It,

instead,producesonlyspecificbrightlycoloredlines,correspondingtospecificwavelengths.Eachwavelengthisassociated

withachangefromoneenergyleveltoanother.Thebiggerthejump,theshorterthewavelength.

OtherThingstoTry

Thespectralbreakdownoflightemittedbyahydrogenatomcanalsobedetectedusingahigh-sensitivitylightsensor,such

asPASCOpartnumberPS-2176.TheresultforthisisshowninFigure120-2.

Table120-1

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Figure120-2Hydrogenemissionspectrum.CourtesyPASCO.

ThePoint

ObservationofseparatecolorsfromglowinghydrogengasconfirmsthemodeloftheatomdevelopedbyNielsBohr,inwhich

electronsoccupyspecificenergylevels.Becauseelectronscannotbebetweentheestablishedenergylevels,manycolors(or

photonfrequencies)arenotproduced.

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Project121

Photoelectriceffect.

TheIdea

In1905,duringhis “miracle year,”AlbertEinsteinpublished fivepapers.These includedspecial relativity,whichdealtwith

spaceandtime,aswellasgeneralrelativity,whichrelatedmassandenergythroughtheequationE=mc2.However,Einstein

wonhisonlyNobelPrizeforworkhedidthatsameyearonthephotoelectriceffect.

Atthetime,itwasknownthatlightshiningoncertainmaterialscouldknockoutelectronstoproduceacurrent.Itstoodto

reasonthatthestrongerthelight,thegreaterthecurrent.Researchersalsofoundthathowmuchofakicktheelectronsgot

(orhowmuchkineticenergytheyhad)dependedonthecolorofthe light.Manyscientistsexpectedastronger lightwould

alsoreleaseanelectronwithgreaterenergy. It tookEinstein’sbrilliancetounderstandwhythecolor (or frequency)of the

lightplayedsuchakeyroleindetermininghowmuchenergytheelectronscameawaywith.Theconsequencesofthisinsight,

alongwiththecontributionsofmanyotherscientists,leadtothedevelopmentofquantummechanics,whichisthebasisfor

themodernelectronicworld.

Figure121-1AlbertEinsteinexplainedthephotoelectricbyclaimingthatlighthadaparticle-likenature.

Thisproject introducesyou to the ideaof thephotoelectriceffectandguidesyou to recreate the typeofdataEinstein

interpreted.

WhatYouNeed

Thebasics

pieceofzincmetal

sandpaperorsteelwool

shortjumperwire

sourceofultravioletlight(acarbonarclamporpossiblyastrong“blacklight”)

sourceofvisiblelight(incandescentlamp)

plateofglass

electroscope,eitherpurchasedorbuiltasaproject

Photoelectriceffectapparatus

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photoelectriceffectapparatus,suchastheDaedelonEP-05(availablefromwww.daedelon.com)

variableDCvoltagesource

voltmeterormultimeterconfiguredasavoltmeter

various light sourcesofknown frequency: this includes laserpointersofknownwavelength, incandescent, carbon

arc,orultravioletlights

colorfilterswithknownwavelengthoftransmittedlight

Method

Thebasics

ThispartintroducesthebasicideaofthephotoelectriceffectandbringsyoutothedilemmaEinsteinaddressed.

1. Rubthepieceofzincwithapieceofsandpaperorsteelwool.Thisremovesoxidestoexposethemetal.

2. Dischargetheelectroscopebytouchingyourfingertotheelectrode.

3. Usingaveryshortjumper,attachthezinctotheelectroscope.

4. Darkentheroom.

5. Shinethelightfromanultravioletsourceontothezinc.

6. Observetheeffectontheelectroscopeleaves.

7. Dischargetheelectroscopeandcomparetheeffectoftheultravioletsourceandthevisiblesource.Alsocompare

theeffectofshiningtheultravioletsourcethroughapaneofglassthattransmitsmostlyvisiblerangelight,buthardly

anyultravioletlight.

8. Chargetheelectroscopepositivelyandobservetheeffectofshiningultravioletlightonthezinc.

9. Chargetheelectroscopenegativelyandobservetheeffectofshiningtheultravioletlightonthezinc.

Photoelectriceffectapparatus

Thisapproachusesametal target inavacuum tube.Because thecurrents thatneed tobemeasuredaresosmall, it is

helpfultohavethedetectorveryclosetothesourceofthecurrent.Thisproceduregoesthroughthegenericstepstomake

this measurement with specific references to the EP-05 operation (more detailed instructions are available with that

apparatus):

1.Setupthefluorescentlamptofocusonthedetector(photodiode).

2.Attachavoltmetertoreadthestoppingvoltage(stoppingpotential)acrossthephotodiode.(Theconnectionsarethe

redandblackbananajacksontheEP-05.)

3.Placethebluefilterovertheopeninggoingintothephotodiode.TheapparatusshouldbesetupasshowninFigure

121-2.

4.Darkentheroom.Ifnecessary,constructalightshieldfromacardboardboxtoprotectthephotodiodefromstraylight.

5.Adjustthestoppingpotential,soalltheelectronsareturnedbackandthereisnophotocurrent.(Thisisaccomplished

byturningthe“voltageknob”tothefullclockwiseposition.)

6.Now,adjustthestoppingpotentialtoitsminimumvalue.(Thiscanbedonebyturningthevoltageknobasfarinthe

counterclockwisepositionaspossible.)

7.Adjusttheradiationintensitybychangingthedistancebetweenthelightsourceandthedetectortoreadabout10on

theintensityscale.Youarenowcalibratedandreadytomakesomemeasurements.

8.Measurethecurrentreadingandwritedownthereadingonthevoltmeter.

9.Inseveralsteps,increasethestoppingpotentialandrecordthecurrentreadingateachstep.Fivereadingsshouldbe

sufficienttodefinealinearrelationship.

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Figure121-2Photoelectriceffectapparatus.

10.ThedatashouldproducealinearrelationshipsimilartotheoneshowninFigure121-2betweenstoppingpotential

andvoltage.

11.Thevoltagerequiredtoproducezerocurrent isakeypointthatdeterminesthevalueoftheworkfunctionforthe

metal(inthephotodiode).

12.Repeatthepreviousstepsusingthegreenfilter.

13.Replacethefluorescentlampwithatungstenincandescentlamp.Installtheredfilterandrepeattheprevioussteps

untilcurrentversusvoltagecurvesfortheredfilter.

14.AlaserorLEDofknownwavelengthcanalsobeusedasasourceofillumination.Adiverginglens(biconcave)may

behelpfulinspreadingthelaserbeamtofilltheopeningareaofthephotodiode.

15.Foreachcolor,plotthecurrentversusvoltageandextrapolatethecurvetofindthethresholdstoppingvoltagethat

resultsinzerocurrent.

16.Plotthestoppingvoltageversusthefrequencyforeachofthefrequencies(colors)forwhichyoutookdata.

ExpectedResults

Ultraviolet light shiningonapieceof zinc results in a charge separation.This chargecauses the leavesof a negatively

chargedelectroscopetoseparatefurtherandcausestheleavesofapositivelychargedelectroscopetocometogether.This

indicatesthechargeisnegativeor,morespecifically,consistingofelectrons.Visiblelightdoesnotresultinthischargebeing

developedinthezinc.

Usingthephotoelectriceffectapparatus,wefindthat:

1. Thegreater the frequency, thegreater thestopping voltage required to limit thecurrent flow.This relationship is

linear.Thismeansthekineticenergyofthefreedelectronsisproportionaltothefrequencyofthelight.

2. Belowacertainthresholdfrequency,nocurrentisgenerated.

3. Increasing the intensity of the light increases the current (for a given stopping potential and light frequency).

However,increasingthelightintensitydoesnothaveanyeffectonthekineticenergyofthefreedelectrons.

4. TheslopeofthestoppingvoltageversusthefrequencygraphrepresentsPlanck’sconstantdividedbythechargeon

oneelectron.Theequationforthisis:

Becausethewavelengthoflightisusuallymorereadilyavailable,thefrequencycanbedeterminedfromtheequation:

frequency=speedoflight/wavelength

5.Fromtheslopeofthevoltageversusfrequencygraph,Planck’sconstantcanbedeterminedfromtheslopemultiplied

bytheelectroniccharge:q=1.6×10−19C.Aslopeof4=10−5givestheexpectedvalueofPlanck’sconstant.

WhyItWorks

Lightcontainsenergybasedonitsfrequency.Thefrequencyofvisiblelightislowerthanthatofultravioletlightanditdoes

nothaveenoughenergy to freeelectrons fromametal,suchaszinc.As the frequencyof the light increases, theenergy

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eachphotoncarriesisraisedabovethethresholdrequiredtofreeelectronsfromthezinc.

Figure121-3Stopping potential for electrons exposed to various frequencies of light. The slope of this line determines

Planck’sconstant.

Theworkfunctionofametalisameasureofhowtightlyelectronsareheldbytheatomsofthemetal.Ifthephotonenergy

isgreaterthantheworkfunctionofthemetal,electronsarereleased. If thefreedelectronsencounterastoppingvoltage

(stoppingpotential),theamountofextraenergyabovetheworkfunctioncanbedetermined.

Thiscanbesummarizedbytheequation:

KE=Ephoton+W

whereKEisthekineticenergyofthefreedelectron(measuredbytheamountofvoltagerequiredtostoptheelectrons).

Ephotonistheenergycarriedbythephoton.

Wistheamountofenergyjusttofreeoneelectronfromthemetalwithnoextraenergytogetitmoving.

Theenergyinaphotonwasgivenby:

Ephoton=hf

wherehisPlanck’sconstantandfisthefrequencyofthelight.

OtherThingstoTry

A good software simulation of the results of this experiment can be found at http://phet-web.colorado.edu/wb-

pages/simulations-base.html.

ThePoint

Thekeyconceptunderlying thisexperiment is that lightenergycomes inspecificamountsorpackagescalledquantaor

photons.Thesephotonscannotbebrokenupintosmallerunits.Thehigherthefrequencyofthelight,thegreatertheamount

of energy contained in one photon. If a photon has enough energy to release an electron, an electric current can flow;

otherwise,belowthatthreshold,noenergywillflow.Themoreenergythephotonhas,themorekineticenergytheelectron

processeswhenitisreleased.

411

Project122

Millikanoil-dropexperiment.Mysterymarbles.Understandinghowtheexperimentworked.

TheIdea

RobertMillikandevisedabrilliant technique toexperimentally determine thechargeof theelectron,which resulted in him

beingawarded theNobelPrize forPhysics.Thisproject letsyou replicateMillikan’s famousexperiment.Basically,Millikan

foundawaytoattachelectronstosmalldropletsofoil,andthenmeasuretheirresponsetoanelectricfield.Becausethisis

amorecomplexexperimentthanmostoftheotherexperimentsinthisbook,itmaybeoutofreachformanyreaders.

For this reasonanotheroption toexplore thisdiscovery isgiven.Oneof theproblemsMillikanhad todealwithwashe

neverknewhowmanyelectronswereonanygivendropofoil.Wecanre-createsomeofthelogicalstepsMillikanfollowed

usingpenniestorepresentelectrons.

WhatYouNeed

Simulation

filmcanistersorplasticprescriptioncontainerswithcovers

spraypaint

about150pennies

digitalscaleorspringbalance

ReplicatingtheMillikanoil-dropexperiment

Millikan’soil-dropapparatus,asshowninFigure122-1

Method

Settingupthesimulatedoildrops

1. Spraypaintorotherwiseobscuretheoutsideofabout8–12plasticcontainers,soyoucan’tseeinside.

2. Measurethemassoftheemptycontainers.

3. Distributeadifferent(random)numberofpenniesineachofthecontainers.

4. Theeasyversionofthisincludesatleastonesetofcontainersthatdifferbyonepenny(suchasContainer7with

12penniesandContainer8with11pennies).

5. A slightly more challenging version is to have no container differing by one penny, but (because of the small

statisticalsample)tohaveatleastonesetofsamplesdifferbytwopenniesandanothersetbytwopennies.

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Figure122-1Millikanoildropexperimentapparatus.CourtesyPASCO.

Findingthechargeofasimulated“electron”(massofapenny)

1. Findthemassofeachcontainerwiththepennies.

2. Subtractthemassofthecontainertoobtainthemassofjustthepenniesineachcontainer.

3. Arrangethemassmeasurementsinorder—smallesttolargest.

4. Subtracteachmassmeasurementfromthepreviousmeasurementinthelist.

5. Identifythesmallest(non-zero)massdifferencebetweenanypairofcontainers.

6. Divideeachofthemassdifferencesbythesmallestmassdifferenceinthelist.

7. Ifanyfractionalnumbersareinthelist,multiplyallthenumberbyafactorthatleavesonlyintegersinthelist.(For

instance,ifoneofthenumbersis1.5,multiplythemallby2.)

8. Makeagraphofthemassdifferencesonthey-axisversustheintegersinStep7.

9. Findtheslopeofthisgraph.Thisshouldgiveyouthemassofthepenny,followingasimilarformof logicMillikan

usedtomeasurethechargeoftheelectron.

TheactualMillikanoil-dropmeasurement

1. Determinethemassoftheoildropbymeasuringthevelocityofthedropasitfalls.Becauseairresistanceaffects

largerdropstoagreaterextent,thevelocityservesasaveryaccuratemeasureofthedropletmass.

2. UsingX-raysoranothersourceofionizingradiation,createarandomnumberofchargesontheelectron.

3. Determine the magnitude of the electric field that just balances the gravitational pull on that droplet. The

gravitational force can be found from themass of the droplet determined in Step 1 and the density of oil. The

greaterthecharge,thegreatertheforceneededtobalanceit.

4. At thispoint,weknow thecharge, butwedon’t knowhowmanyelectronsareonanygivendroplet.This is very

similartothesituationwejustaddressedwiththepennies.Althoughwedidnotknowhowmanypennieswereinany

particularcontainer,wewereabletofindthemassofasinglepenny.Usingasimilarlogic,Millikanwasabletofind

themassofanelectron.

ExpectedResults

Followingtheprevioussimulatedprocedureusingpennies, theslopeof the line inFigure122-2 is2.7grams,which is the

massofasinglepenny.Thisisareasonableaverageforpenniesmintedbeforeandafter1982.Amoreprecisevaluecan

413

beestablishedbysortingpenniesintogroupsbeforeandafter1982.

ThechargeofanelectrondeterminedbyMillikanis–1.6×10−19Coulombs.

OtherThingstoTry

MarblescanbeusedtosimulatethelogicalprocesspursuedbyMillkaninasimilarmannerthatwasdonewithpennies.The

marbleshaveagreatermass,whichmaymakeiteasiertodetectdifference.However,findingarelationshipgraphicallymay

bemoredifficultbecauseofthevariationinmassforarandomsetofmarbles.

Figure122-2Usingthemassofapennytosimulatethephotoelectriceffect.

WhyItWorks

Thesizeofanoildropisfoundbyobservingitsfree-fallvelocityinair.Theoildropisthengivenachargebyexposingitto

ionizingradiation.Theelectricfieldthatestablishesequilibriumwithgravityisrelatedtotheforce.Althoughtheexactnumber

ofelectronsonanygiveoildropcannotbedetermineddirectly, thecommonmultiple leadsus to identify thechargeofa

singleelectron.

ThePoint

TheMillikanoil-dropexperimentdeterminesthechargeofanelectronbymeasuringtheresponseofanoildropchargedby

electronsinanelectricfield.

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Project123

Ping-pongballchainreaction.

TheIdea

Thisisafunandsimpledemonstrationthatwillhelpyouunderstandhowanuclearchainreactionoccurs.Itwasusedyears

agoinaWaltDisneyfilmcalledOurFriendtheAtomandappealstoallreadersincludingtheyoungestandtechnicallyleast

sophisticated.

WhatYouNeed

24spring-typemousetraps

49ping-pongballs

enclosurewithatleastonetransparentside(alargefishtankwithglasssidesandaglassbottomcanworkwell)

optional:2mirrorsthesizeof,orlargerthan,thesideoftheenclosure

Method

1.Setthetraps(Figure123-1).

2.Carefullyplacetwoping-pongballsoneachofthemousetraps(wherethecheesewouldhavegone).SeeFigure123-

2.

3.Layoutthemousetrapsinanarraythatwillfit intotheenclosure,suchasa6×4array.Obviously,youneedtobeextremelygentleandavoidsuddenmotionstopreventaprematurereleaseof themousetrap.Anymishapwill likely

takeothermousetrapsoutwithit.

4.Eitherlowertheenclosureoverthemousetrapsordevelopawaytobringthemousetrapsintotheenclosure.Youmay

need toexperimentwithdifferentmethodsof loading themousetraps.Youmayprefer toplace theping-pongballs

after,ratherthanbefore,movingthetraps.Youmaywanttodevelopawoodenorfoamboardtemplatethatprotects

thetrap’striggermechanismwhileyouareplacingtheping-pongballsorgluethetrapstoaboard.

Figure123-1Eachmousetraprepresentsauraniumatom.

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Figure123-2Eachpingpongballrepresentsaneutron.

5.Withtheping-pongballloadedonthemousetrapsintheenclosure,youarereadytoinitiatethechainreaction.Sofar,

you have used 48 ping-pong balls, so one should be left. The remaining ball is the neutron that starts the chain

reaction.

ExpectedResults

As inanuclear-fissionchainreaction,aneutron(thestarterping-pongball)createsthefirstfissionreaction.Thisevent is

simulatedbythemousetrapreleasingtwoadditionalping-pongballs.These,inturn,potentiallyeachreleasetwomoreballs

(neutrons)initiatingadoublingoftheavailableneutronswitheachfission.Asadditionalping-pongballsarereleased,therate

ofthereactionaccelerates.Thischainreactionissimulatedbyrapidlyreleasingpingpongballs,whichinturnreleasesother

ping-pongballstocontinuethereaction.TheaftermathofthisisshowninFigure123-3.

Figure123-3Afterasimulatedchainreaction.

WhyItWorks

Nuclearfissionoccursinnaturewhenanisotopeofanuclearmaterialabsorbsaneutronandbecomeunstable.Thenucleus

splits, forming two lighter “daughter”nucleiandasprayof freeneutrons thatproduces thecascadingeffectknownasa

chainreaction.Therealsoneedstobeacriticalmassforthisprocesstobecomeself-sustaining.

416

OtherThingstoTry

Itwouldbeinterestingtocaptureavideoimageofthissimulatednuclearreactionandviewitinslowmotion.

ThePoint

Nuclear fission is initiatedbya freeneutron thatcausesanucleus (suchasauranium-238nucleus) tosplit and release

additionalneutrons.Thisisthebasisofnuclearpower,whichcurrentlyprovidesaboutone-fifthoftheelectricityintheUnited

States.

417

Project124

Thesodiumdoublet.Whydowethinktheelectronhasbothupanddownspins?

TheIdea

Noonehaseverseenanelectronspin. In fact, for thatmatter,noonehaseverevenseenanelectron.Yet,weknowan

electronbehavesasifitwerespinning.Someofthemostrevealingevidenceforthiscomesfromthelightthatcertainatoms

emitwhenthey’reexcited.

Ifsomesodiumchlorideisexposedtoaflame,theflametakesonacharacteristicyellow/orangecolor.Thisisthecolor

observedinthecommonflametestusedinchemistrylabstoidentifythepresenceofsodiuminsodiumvaporstreetlamps.If

youlookatthelightcomingfromanexcitedsodiumatomwithaspectroscopeordiffractiongrating,thefirstthingyounotice

isasingleorange/yellowlinewithawavelengthbetween589and590nanometers.

However,oncloser inspection,younoticenotonebuttwoorange/yellowlines.Thepurposeofthisproject istoobserve

thesetwolines,knownasthesodiumdoublet,and,moreimportantly,tounderstandwhytheyaresplit.

WhatYouNeed

Bunsenburnerorotherflame

concentratedsodiumchloridesolution

cleannichromewireloop(orawoodensplint)

diffractiongratingorspectroscope

sodiumvapordischargetubewithappropriatehigh-voltagepowersupply

Method

1. Useoneofthepreviousmethodstoproducealightsourcegeneratedbyexcitedsodiumatoms.

2. Darkentheroom.

3. Observethelightusingadiffractiongratingoraspectroscope.

4. Lookcarefully until you seea vertical yellow/orange line. Lookclosely until you notice this line is formedby two

separatelines.SeeFigure124-1.

ExpectedResults

Thepointofthisprojectistoobservetwoseparateyellow/orangelinesthatmakeupthesodiumdoublet.

WhyItWorks

When an electron goes fromone energy level to a lower energy level, it gives off light. Each energy level can hold two

electrons:onewithspinupandtheotherwithspindown.Theelectronwiththespinuptakesaslightlygreateramountof

energy togo fromoneenergy level toanother.Asa result, theelectronswithdifferent spinconditionsgiveoffa slightly

differentcolor(wavelength)light.

ContinuingtheNewJerseyTurnpikeanalogy(fromProject120),let’ssayyoutravelacertaindistancegoingfromExit7to

Exit 8. But things are slightly different if you get off at either an eastbound or westbound ramp at the exit. That small

differencecanbethoughttobesomethingliketheeffectcausedbyelectronspin.

418

Figure124-1Electronsinasodiumatomproduceaprimarycharacteristicwavelengthwhenelectronsmovefromoneenergy

leveltoanother.Aslightlydifferentwavelengthisproduceddependingonwhetherthespinoftheelectronis“up”or“down.”

OtherThingstoTry

Ifanexcitedsodiumatomisexposedtoaverypowerfulmagneticfield,thesespectrallinessplitevenfurther.Thisiscalled

theZeemaneffect,which requiresmagnetic fieldson theorderof18Teslas.However, because this is roughly20 times

morepowerful than the very strongmagnetic fieldsused tostudynuclearmagnetic resonance,wewon’t pursueZeeman

splittingexperimentsinthisbook.

ThePoint

Inanatom,electronshaveupordownspin.Whenanelectrongoesfromoneenergyleveltoanother,theenergygivenoffby

eachofthetwospinorientationsisslightlydifferent.Observingthesplit inthefrequencysupportstheconceptofelectron

spin.

419

Project125

Buildingacloudchamber.Whymuonsshouldnotbehere.Specialrelativity.

TheIdea

Cosmicrays are subatomic particles that stream through the universe at high speed. As you read this, dozens of these

particlesarepassingthroughyourbodyharmlesslyeverysecond.Inthisproject,youbuildadevicecalledacloudchamber,

whichwillmakesomeof theseparticlesvisible.Thecloudchambercontainsanalcoholvaporcloud thatproducesvapor

trailswhenachargedparticlepassesthroughit.Thistrailrevealsthepathortracktheparticlestakeastheypassthrough

thevaporcloud.Youbegintolearntorecognizethesignatureofsomeofthoseparticles.

Scientistsbelievemostcosmicrayscomefromthesun.Thesecosmicraysconsistoffragmentsofthenucleiofhydrogen

orheliumatoms,resultinginparticlesthatareeithersinglycharged(protons)ordoublycharged(alphaparticles).Whenthese

cosmic rayparticlesstrike theupperatmosphereof theEarth, theycollidewith theairmoleculespresent.This results in

collisionsthatproducenewparticles,calledsecondarycosmicrays.Thesearewhatyouwilldetectinyourcloudchamber.

Themostcommonresultofthecollisionisaparticlecalledamuon.Themuonisanegativelychargedparticle,whichis

bigger thananelectron,butsmaller thanaproton.Themuons thatarecreated in theupperatmospheredecay incredibly

rapidly.Becauseoftheirextremelyshortlife,theyshouldnotbeabletosurvivethetripthroughtheEarth’satmospheretobe

detectedonitssurface.However,themostcommonparticledetectedinthesecondarycosmicraystreamisthemuon.The

onlyway toexplain theabundanceofmuonsyousee inyourcloudchamber isby turning toEinstein’s theoryof relativity,

whichsaysthattimeslowsdownfortheveryhigh-speedmuons.

AlsopresentintheshowerofsecondarycosmicrayshittingtheEarth’ssurfacearepositronsandelectrons.Thepositrons

areaformofantimatterthatcanalsobeseeninyourcloudchamber.

WhatYouNeed

small2.5gallonfishtank

smallStyrofoamcooler

1literofpureisopropylalcohol(not70percentalcohol,asismorereadilyavailable).Puremethylalcoholcanalso

beused.

sheetofblackfelt largeenoughto linethebottomofthetank(note, thefishtankwillbeturnedupsidedown,so

whatwerefertoasthebottomofthefishtankwillbecomethetopofthecloudchamber)

metalplatethesizeofthetopofthefishtank—aluminumispreferablebecauseitconductsheatbetterthansteel

ducttape,siliconerubbersealant,orweatherstrippingtomakethefishtankairtight

black(solventresistant)paint

about1poundofdryicetoencasethebottomofthefishtank

brightlightsource,suchasapowerfulflashlight

strongmagnet

optional: source of low-level radiation, such as a smoke detector,mantle of oldColeman lantern, or certain old

ceramicobjectsthatcontaincobalt

optional:adigitalvideocamera

Method

Buildingthecloudchamber

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1. Becausethedryicehasalimitedshelflifeand,formostusers,takesaspecialefforttoobtain,agoodideaistodo

adry runandassemble theseparts beforepickingup thedry ice.Also, rememberdry ice isextremely coldand

shouldnotcomeintocontactwitheyesorskin.

2. Attachtheblackfelttothebottomofthefishtank.UseblackelectricaltapeorVelcrounderthefelttosecureit,so

itremainsinplacewhenthefishtankisinverted.Youmaywanttodevisesomeotherwaytosecurethefeltsuchas

smallwoodensupports.Keepinmindthatwhateveryouusetosupportthefeltmustnotbedegradedbythesolvent

vaporthatwillbepresent.AsolventresistantgluesuchasGorillaGlueorGorillatapecanholdthefeltwithoutbeing

attackedbythealcoholvapor.

3. Placethedryiceinthebottomofthecooler.Ifthedryiceisinlargechunks,youwillhavetochopit.Youcanadda

littlealcoholtothemixturetoformaslushtomakebetterthermalcontactwiththemetalplate.Ifyoudon’thavea

coolerthefishtankwillfitin,useaboxandlineitwithinsulatingmaterial.

4. Soaktheblackfeltwithalcohol.Avoiddrippingthatproducespuddlesofalcoholonthemetalplatebynotusingtoo

muchalcohol.

5. Cover thedry icewith themetalplate,with thesidepaintedblackfacingawayfromthedry ice.Themetalplate

shouldbecompletelyincontactwiththedryice.Youcansecuretheplatetothetankfirstifthatworksbetter.

6. Place the tank—alcohol-soaked felt up—with the metal plate over the dry ice. It is important to establish good

thermal contact between the dry ice and themetal plate. People have used solid blocks of dry ice as well as

crushedice.Goodthermalcontactcanbeachievedbycreatingaslurrybymixingsomeisopropylalcoholinwiththe

dryice.Ifyoucrushthedryice,besuretowearprotectiveclassestoavoidextremelycolddryicefragmentsfrom

contactingyoureyes.Thedryicemixedwithalcoholshouldbearound−70degreesCor−94degreesF.7. Sealthechamberabovethemetalplatebywrappingelectricaltapearoundtheedgewherethemetalplatemeets

thefishtank.(Somepeoplehavefoundthatpouringasmallamountofisopropylalcoholinthechannelsurrounding

themetalplatehelpsformanairtightseal.)Ifairisdrawnintothechamber,thevaporcloudmaynotfromproperly.

8. Itmaybenecessarytokeepthetopofthecloudchamber(wherethealcohol-saturatedfeltis)fromgettingtoocold.

The bottom of the chamber should be near −60 degrees C (−76 degrees F) to enable the formation ofsupersaturated vapor. However, the top of the chamber should be maintained close to room temperature (22

degreesCor72degreesF)topromoteevaporationofthealcohol.Toaccomplishthisitmaybenecessarytowarm

the top of the chamber either with your hands or with some other means to maintain the proper temperature

gradient.Itmightbehelpfultomeasurethetemperaturesofbothsurfaces.

9. Shinethelightfromthesideofthetanktowardthemetalplate.

10. Thestackshouldlooklikethis,fromtoptobottom:

–Bottomofthefishtank

–Blackfeltsoakedwithisopropylalcohol

–Fishtank(metalplatecoveringthetopofthetank)

Figure125-1Cloudchamberassembled.

–Metalplate

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–Sheetsofdryice

–BottomoftheStyrofoamcooler

Observingtracks

1. Atfirst,youwillnoticeamistofalcoholdropletsforminginthetank.

2. Afterabout15minutes,youshouldstarttoseethetracksofparticlespassingthroughthevaporafewcentimeters

abovethebaseplate.

3. Itmay be helpful to view the tracks by looking toward the light source at an angle so that the vapor trails are

illuminatedfrombehind.

4. Ifyouhavea low-levelradiationsource(suchasoneoftheeverydayobjectsmentionedintheparts list),placeit

near the edge of the cloud chamber and compare its effects to cosmic rays. (Smoke detectors have low-level

radioactivematerials,suchasamericium,thatarepackagedsafetyforitsintendeduse.Donotattempttodismantle

asmokedetector togetat the radioactive isotope.Themantle forat leastsomeColemangas-camper lanterns

containstracesofradioactiveThorium,whichcanalsobeasafelow-levelsourceofchargedparticlestoview.)

5. Observewhatamagnetdoestothetracks.Noteinparticularhowtheparticleisdivertedinrelationtotheparticle’s

originalvelocityandthenorth-to-southdirectionofthemagneticfield.

6. Onceyougetthisgoing,avideocameracanbeveryhelpfulinrecordingthetracksandprovidinganopportunityto

analyzethetracksindetail.Stillphotographyisverydifficultbecauseoftherandomnessofthewaythetracksare

createdandtherapiditywithwhichtheyfade.Extractingstillimagesfromavideorecordingismorelikelytoproduce

clearimagesoftracks.

ExpectedResults

Afterthemistformsintoasupersaturatedalcoholvapor,youmaystarttonoticetracksthatlooklikespiderwebsalongthe

chamberbottom.Thesearecosmicraysandshouldbenoticeableroughlyseveraltimeseachminute.

Alpha particles, which are two protons and two neutrons bonded together, form sharp, well-defined tracks about 1

centimeterlong.

Betaparticles,whichconsistofelectrons,havethinnerandlongertracks,roughly3to10centimetersinlength.

Someofthetracksmaycomeinstraightandthensharplybreakinadifferentdirection.Anexampleofthis isshownin

Figure125-2,whichshowsamuonbeingdeflectedasitdislodgesanelectronfromanairmolecule.

422

Figure125-2Collisionbetweenamuonandanatom.Themuonisdeflectedandtheelectron isknockedoutoftheatom,

leavingasecond,faintertrack.

Atrackthatstarts inastraight line,butthenbreaksoffatasharpangle,suchasshown inFigure125-3,most likely is

muondecayduringwhichamuonspontaneouslydecaystoformanelectron.Theelectronisvisibleasathinnertrack.The

twoneutrinosdonotformvaportrailsandarenotvisiblebecausetheyarenotcharged.

Figure125-3Muondecay.Amuon spontaneously decays intoanelectronand twoneutrinos.The neutrinos do not leave

tracksinthecloudchamber.

Youmayseeaveryjagged,erraticpathrepresentingalow-energyparticlebeingscatteredmultipletimes.Thisispictured

inFigure125-4.

Ifyouviewthechamberfromthefront,withtheparticlescomingfromtheleft,andthemagnet’snorthpoleatthetopof

thechamber,particlesbendingtowardthebackofthechamberarepositivelychargedparticles(suchasprotons).Particles

bendingtowardthefrontofthechamberarenegativelycharged.

WhyItWorks

Someof the radiation in cosmic raysor isotope sourcesconsistsof chargedparticles.As thesechargedparticlespass

through thesupersaturatedalcohol vapor in thechamber, theparticle ionizes themoleculesof thevapor.Dropletsof the

vaporthencondenseonthepathleftinthewakeoftheparticle’spath,leavingavisibletrail.

Figure125-4Zigzagpathofslowmovinglow-energychargedparticles.

Collisionsoccurthateitherchangethemotionoftheparticleorresultinasubatomicevent,whichresultsinawholenewmix

of particles. The laws of conservation of momentum and mass must be followed, which helps to identify the particles,

includingthosethatarenotvisible.Nonionizedparticles,suchasneutrons,willnotleaveavisibletrack.

Figure125-5showsasamplingofparticlecollisionsinamoreelaboratedetectionsystem,calledabubblechamber.

OtherThingstoTry

Amuon isoneofmanytypesofsubatomicparticlesthatmaybedetectedbyyourcloudchamber.Amuonhasthesame

chargeasanelectron,butitis207timesmoremassive.Muonsarecreatedwhencosmicraysstriketheupperlayersofthe

Earth’satmosphere.Muonsareunstableanddisintegrateintootherparticlesalmostimmediately.

423

After being created at the top of the atmosphere, muons decay within 2.2 microseconds or 0.0000022 second. A

microsecondisone-millionthofasecond.Inthistime,themuonwouldtravelonly659meters(0.659km).Becausetheyare

createdbetween10and15kmabovethesurfaceoftheEarth,mostmuonswoulddecaybeforereachingthesurfaceofthe

Earth.Thetroubleishowisitevenpossiblethatmuonsareabletotravelthedistancefromwheretheyarecreatedatthe

topoftheatmospheretothegroundbeforedecaying?Eventravelingatover99percentofthespeedoflight,themuonsdo

nothaveenoughtimetomakeittotheground.Weshouldnotseeanymuonsatall.

Figure125-5Subatomicparticletracks.CourtesyBrookhavenNationalLabs.

However,becausethemuonsaretravelingsofast—accordingtoEinstein’stheoryofrelativity—timeslowsdownforthem.

ThefactthatwecanobservemuonsatthesurfaceoftheEarthservesasproofofEinstein’stheory,whichstatesthatthe

timeforthemovingparticleis

wheretisthetimethemuontakesasobservedfromtheEarth,to isthetimeitwouldtakeforastationarymuon,v isthe

speed of the particle which, in this case, is 0.99c, and c is the speed of light.When viewed through the perspective of

Einstein’stheory,themuon’slifetimebecomeslarger(35microseconds),whichgivesitenoughtimetomakeitthroughthe

Earth’satmospherebeforedecaying.

Anothertrackyoumayseeisthatofapositron,whichismoredifficulttodistinguishfromotherpositivelychargedparticles.

However,justknowingthatmanyofthecloudchambereventsarepositronsissignificantinitself.Apositronistheantimatter

versionofanelectron.Now,beforeyoudismissthisasafar-fetchedcontributionfromsciencefiction,thepositron isvery

commonly found incollision fragments fromcosmic rays. (By theway, if youareascience-fiction fan,antimatterplaysa

prominentroleinDanBrown’sAngelsandDemons.)Whenapositroncollideswithanelectron,thetwoannihilateeachother

andreleaseenergy.Althoughitmaybedifficulttoidentifythisevent,yourcloudchamberpositron-electronannihilationsare

common. This subatomic particle process has actually been developed into a useful application in the form of the PET

scanners found inmanymedical imaging labs.TheP inPETstands for “positron.”Today, thePETscansenablemedical

researchersanddiagnosticianstoimagefunctions,suchasthemetabolismofmalignanttumorsandtheearlydiagnosisof

Alzheimer’sdisease,andtoidentifyriskfactorsforheartconditions.

Althoughthetechnologicalapplicationsofpositronannihilationarecomplex, theyarethesameeventsyoucanobserve

takingplaceinyourcloudchamber.

(Backgroundonsubatomicparticlesandtheirdetectionwasderivedfromthefollowingsource,whichisrecommendedfor

further informationon this topic: “CloudChambersandCosmicRays,A LessonPlanandLaboratoryActivity for theHigh

School Science Classroom,” Cornell University, Laboratory for Elementary Particle Physics, 2006, available from

424

http://www.lepp.cornell.edu/Education/rsrc/LEPP/Education/TeacherResources/cloudchamber.pdf.)

ThePoint

Cosmicrays,consistingofchargedsubatomicparticles,arecontinuouslystrikingtheEarth’ssurface.Theseparticlescanbe

detectedbyobservingthetrackstheyleaveinasupersaturatedvaporinadevicecalledacloudchamber.

425

AppendixA

WheretoGetStuff

PASCOScientific

10101FoothillsBlvd.

Roseville,CA95747-7100

1-800-772-8700

www.pasco.com

Sargent-Welch

P.O.Box4130

Buffalo,NY14217

1-800-727-4368

www.sergentwelch.com

FlinnScientific,Inc.

P.O.Box219

Batavia,IL60519

1-800-452-1261

www.flinnsci.com

FreyScientific

c/oSchoolSpecialtyScience

80NorthwestBlvd.

Nashua,NH03063

1-800-225-3739

www.freyscientific.com

EdmundScientific

60PearceAve.

Tonawanda,NY14150

1-800-728-6999

www.scientificsonline.com

DaedalonCorporation

P.O.Box727

Waldoboro,Maine04572

1-800-299-5469

www.daedalon.com

RadioShack

www.radioshack.com

426

AppendixB

(MoreThan)EnoughPhysicstoGetBy.(HighlyOptional)

Equations

Project1

v=Δd/Δt

Project2

d=do+vt

Project3

d=do+v(t–to)

Project5

F=ma

Project8

Project9

v=R/t

R=(v2/g)sin2θ

h=(vsinθ)2/2g

Project10

vx=R/t

Project13

427

Project17

Project19

g=2d/t2

a=2d/t2

Project22

Project31

Project51

Project56

Project67

Project68

Project70

f=v/2(L+0.8d)

Project77

v=λf

v=331+0.6T

Project81

428

Project83

Project85

nisin(θi)=nrsin(θr)

Project86

I/Io=cos2θ

Project96

wherekistheCoulombconstant=9.0×109m2/C2

Project100

Ohm’slaw

V=RI

R=VI,and

I=V/R

Rseries=R1+R2

1/Rparallel=1/R1+1/R2+…

Project103

ThecurrentforachargingcapacitorisgivenbyI=Ioe−t/RC

ThevoltageforachargingcapacitorisgivenbyV=Vo(1–e−t/RC)

ThecurrentforadischargingcapacitorisgivenbyI=Ioe−t/RC

ThevoltageforadischargingcapacitorisgivenbyV=Voe−t/RC

Project116

I=IoeqV/kT

Project121

Ephoton=hf

Project125

429

Unitsusedinthisbook

Length

1m=3.28ft

1mile=1.61km

1inch=2.54cm

Time

1day=86,400s

1year(365¼days)=3.16×107s

EnergyandPower

1J=0.738ft-lb=0.239cal

1kW-hr=3.6×106J1W=1J/s

1hp=746J

Force

1N=0.225lb

1lb=4.45N

Weightandmass

A1kgmasshasaweightof9.8N(onEarth)

A1kgmasshasaweightof2.2lbs(onEarth)

Speed/velocity

1m/s=2.24mi/hr

1km/hr=0.621mi/hr

1km/hr=0.278m/s=0.91ft/s

Volume

1cc=1cm3=1mL

1liter(l)=1000cm3

1gal=3.79liters

Pressure

430

1Pa=1N/m2=1.45×10−4lb/in2

1atm=1.01×105Pa=14.7lb/in2(psi)

=760mm-Hg

=760torr

Examplesofprefixes

1km=1000m

1kg=1000g

1m=100cm=1000mm

1liter=1000mL

1μm=1×10−6meter1nm=1×10−9meter1megohm=1×106ohm

431

Index

absolutezero

acceleration

directionof

andforce

gravitationdeterminedbyapendulum

measuredbyGalileo

measurementof

accelerometer

airpressure

airtrack

Aleo,Chris

alligatorclip

alphaparticles

alternatingcurrent(AC)

AmericanWireGauge(AWG)

americium

ammeter

angle

ofreflection

ofrefraction

ofrepose

angularvelocity

antimatter(AngelsandDemonsbyDanBrown)

Archimedes’principle

astronauts

Apolloastronauts

Atwood’smachine

balloon

ballparkestimate

Bardeen,John

basketball

battery

BCStheory

beatfrequency

bedofnails

Beatles,The

Bernoulli,Johann

betaparticles

bigG

birds(andNewton’sthirdlaw)

blowdryer

Bohr,Niels

bottlerocket

bowlingball

Brachistochrone

Bradbury,Ray

breakdownvoltage

432

Brewsterangle

BrookhavenNationalLabs

bulb,light

Christmastree

electroscope

induction

neon

numberofphotons

bullet

buoyantforce

buzzer

calculator

candle

capacitor

Cartesiandiver

Cash,Johnny

cathoderaytube(CRT)

Cavendish,Henry

centerofgravity

centerofmass

ceramic

hotplatetop

radioactive

superconducting

CERN

chainreaction

Charles’law

circuit

cloudchamber

coefficient

offriction

ofvolumeexpansion

collision

elastic

inelasticcollision

productionofcosmicrays

subatomicparticles

compressor,air

computers

conservation

conservation

ofangularmomentum

oflinearmomentum

Cooper,Leon

Copernicus,N.

copper

corkgun

CornellUniversity

cosmicrays

coulomb

433

CRT

CSI

current

cycloid

DaedalonCorporation

DataStudio

DCpowersupply

DeGregorio,Brad

diffraction

diffractiongrating

diode

discovery

displacement

dollar

Dopplereffect

doubleslitexperiment

Dragoiu,T.

drum-gallon

dryice

dumbbells

Earth

atmosphere

magneticfieldof

massof

EasyScreen

eddycurrent

EdmundsScientific

Einstein,Albert

generalrelativity

photoelectriceffect

specialrelativity

Eisenhower,DwightDavid

EleanorRigby,byTheBeatles

electronspin

electroscope

elevator

ElihuThomson,ringtosser

ellipse

energy

equilibrium

ESPN

Excel.

fancar

Faraday,Michael

feather

fishtank

FlinnScientific

force

centrifugal(fictitiousforce)

434

centripetal

electrostatic

friction

gravity

magnetic

free-fall

frequency,

beat

fundamental

natural,resonant

overtone

FreyScientific

friction

GalileoGalilei

galvanometer

Gay-Lussacapparatus

generalrelativity

GorillaGlue,Tape

Grabowski,Stephen

gravity

gravitywell

Greenland

gyroscope

happy/sadballs

heatoffusion,latentheat

Hovercraft

HoverPuck

hydrogen

hydrogentube

ice

implodingcan

impulse,andmomentum

indexcard

index

ofrefraction

ofrefraction,variable

induction

inertia

insulatedwire

interference,

constructiveinterference

destructiveinterference

interferencepattern

iron

Kepler’slaw

kineticenergy

andphotoelectriceffect

laser

435

latex

leafblower

lens

Lenz’slaw

Leydenjar

light

intensity

meter

monochromaticlight

polarized

speedof

totalinternalreflection

lightemittingdiode(LED)

lightning

liquidnitrogen

Lissajouspattern

littleg

logarithmicscale

Maglevtrain

magnet

accelerationfrom

bendingcosmicrays

braking

cosmicraybendingfrom

cube

neodymium

toholdlensonchalkboard

usedinmotor

magneticfield,

ofEarth

onacurrentinawire

onanelectronbeam

induction

levitation

sensor

shapeof

magneticresonanceimaging(MRI)

magnifyingglass

Malus’slaw

marshmallow

mass

Maxwell,JamesClerk

Meissnereffect

MichiganStateUniversity

microphone

microwaveoven

milk

Millikan,Robert.

Mingdynasty

mirror

436

Misniak,Tom

momentofinertia

momentum

monkey(andcoconut)

moon

motionsensor

mousetrap

multimeter

muon

Mythbusters

NASA

neonbulb

neutralbuoyancy

neutron

NewJerseyTurnpike

Newton’scradle

Newton,SirIsaac

firstlaw

secondlaw

thirdlaw

NobelPrize

non-magneticmaterial

NorthPole

Oersted,Hans

Ohm’slaw

oil-dropexperiment.SeeMillikan,Robert

opticalfibers

optics

oscilloscope

OurFriendtheAtom,byWaltDisney

painteronscaffoldproblem

papercup

PASCOScientific

Peltiereffect

pendulum

period

phasechange

photoelectriceffect.SeeEinstien,Albert

photon

ping-pong

Pisa,LeaningTowerof

Planck’sconstant

plasmaglobe(SunderBall)

PlayDough

pokerchips

polarizingfilters

positron

positronemissiontomography(PET)

potentialenergy

437

powersupply.SeeDCpowersupply

pressure

defined

projectile

atanangle

defined

footballas

horizontalprojectile

launcher

monkeyandcoconut

protractor

pulley

Pythagoreanformula

quantummechanics

RadioShack

rectangularprism

reflection

refraction

defined

resistance

copper

iron

measurement

resonance,resonantfrequency

right-handrule

ringtosser

rippletank

rubberrod

safety

sailboat

Sargent-Welch

satellite

Schrieffer,John

SCUBA

SearsTower

Seebeckeffect

semiconductorheating

seriescircuit

shavingcream

Silver,Dan

skydivers

smokedetectors

Snell’slaw

sodiumdoublet

solarcell

solderingiron

sound

meter

speedof

438

SouthPole

spark

specialrelativity

specificheat

spirograph

spreadsheet.SeeExcel

spring

springconstant

Sputnik

standingwave

staticcharge

staticequilibrium

staticfriction

stopwatch

subatomicparticles

suctioncup

Sunderball(PlasmaGlobe)

sunglasses

superposition.Seealsointerference

supersaturatedvapor

cloudchamber

tablecloth

temperaturesensor(thermocouple)

terminalvelocity

teslacoil

Thanksgivingdinner

thermometer

ThomasYoung,doubleslitexperiment

Thomson,Elihu

Thomson,J.J.

thorium

tightropewalkers

tonegenerator

toolbin

torque

Torricellibarometer

transversewave

truck(birdsflyingin)

tugofwar

tuningfork

turntables

UniversityofMaryland

uraniumatom

USBport

vandeGraaffgenerator

Velcro

velocity

average

constant

439

andkineticenergy

measurement

andmomentum

ofoildrop

relationshipwithcentripetalforce

ofsatellite

usedtofindrangeofaprojectile

versustime

ofwave

videocamera

voltage

voltmeter

AC

DC

Voyager

wave

electromagnetic

light

longitudinal

sound

transverse

waveformgenerator

wavelength

weightless

Wimshurstmachine

workfunction

yardsale

YBa2Cu3O7

Young,Thomas

Zeemaneffect

440

TableofContents

Introduction 12

Section1Motion 19

Project1Gettingstarted.Constantvelocity.Runningthegauntlet 19

Project2Picturingmotion.Gettingamoveon 23

Project3Thetortoiseandthehare.Playingcatch-up 27

Project4Howdoesasailboatsailagainstthewind?Componentsofforce 30

Project5Steppingonthegas 35

Project6Rollingdownhill.Measuringacceleration 38

Project7Independenceofhorizontalandverticalmotion.Basketballtossedfromarollingchair 41

Project8Targetpractice.Horizontalprojectile—rollingoffatable 44

Project9Takingaim.Shootingaprojectileatatarget 47

Project10Mondaynightfootball.Trackingthetrajectory 51

Project11Monkeyandcoconut 55

Section2GoingAroundinCircles 60

Project12Whatisthedirectionofasatellite’svelocity? 60

Project13Centripetalforce.Whatisthestringthatkeepstheplanetsinorbit? 62

Project14Agravitywell.Followingacurvedpathinspace 70

Project15Howfastcanyougoaroundacurve?Centripetalforceandfriction 72

Project16Ping-pongballsracinginabeaker.Centripetalforce 74

Project17Swingingapailofwateroveryourhead 77

Section3Gravity 80

Project18Featherandcoin 80

Project19Howfastdothingsfall? 84

Project20Thebuckstopshere(thefallingdollar).Usingametersticktomeasuretime 90

Project21Weightlesswater.Losingweightinanelevator 93

Project22Whatplanetareweon?Usingaswingingobjecttodeterminethegravitational

acceleration97

Section4ForceandNewton’sLaw 100

Project23Newton’sfirstlaw.WhattodoifyouspillgravyonthetableclothatThanksgivingdinner 100

Project24Newton’sfirstlaw.Pokerchips,weightonastring,andafrictionlesspuck 103

Project25Newton’ssecondlaw.Forcinganobjecttoaccelerate 106

Project26Newton’sthirdlaw.Equalandoppositereactions 111

Project27Newton’sthirdlaw.Bottlerockets.Whydotheyneedwater?(SirIsaacNewtoninthe

passenger’sseat.) 114

441

Project28Pushingwater.Birdsflyinginsideatruck 117

Project29Slippingandsliding 119

Project30Springs.Pullingback.Thefurtheryougo,theharderitgets 121

Project31Atwood’smachine.Averticaltugofwar 123

Project32Terminalvelocity.Fallingslowly 126

Project33Balancingact.Painteronascaffold 129

Project34Hangingsign 132

Project35Pressure.Implodingcans 135

Project36Pressure.Supportingwaterinacup 138

Project37Pressure.Sometimesthenewscanbeprettyheavy 140

Project38Archimedes’sprinciple.Whatfloatsyourboat? 143

Project39Cartesiandiver 145

Project40Anair-pressurefountain 147

Project41Blowingupamarshmallow.Lessiss’more.Whyastronautsdonotuseshavingcreamin

space151

Project42Relaxingonabedofnails 153

Project43Blowinghangingcansapart.WhatBernoullihadtosayaboutthis 156

Project44Centerofmass.Howtobalanceabroom 159

Project45Asimplechallenge.Moveyourfingerstothecenterofameterstick 161

Project46Centerofgravity.Howfarcanastackofbooksextendbeyondtheedgeofatable? 164

Project47Centerofmass.Theleaningtowerofpizza 167

Section5Energy/Momentum 172

Project48Thependulumandyourphysicsteacher’sMingdynastyvase 172

Project49Twoslopes.Differentangle,sameheight 174

Project50Racingballs.Thehighroadversusthelowroad.Whichwins? 177

Project51Linearmomentum.Wherecanyoufindaperfect90-degreeangleinnature? 182

Project52Elasticcollisions 186

Project53Inelasticcollision.Stickingtogether 189

Project54Impulseandmomentum.Eggstremephysics 192

Project55Usinggravitytomoveacar 194

Project56HowcanCSImeasuremuzzlevelocity?Theballisticpendulum 196

Project57Angularmomentum.Ridingabike 198

Project58Momentofinertia.Iceskatersanddumbbells 200

Project59WhatcausedVoyagertopointinthewrongdirection? 203

Project60Momentofinertia.Thegreatsoupcanraceorthat’showIroll 206

Project61Makingwaves.IthoughtInodethis 208

442

Project62Rollinguphill 212

Project63Gettingaroundtheloop.Fromhowfarabovethegrounddoestherollercoasterneedto

start?215

Section6SoundandWaves 218

Project64Whatdoessoundlooklike?Oscilloscopewaveforms 218

Project65Rippletank 228

Project66Simpleharmonicmotion.Theswingingpendulum 232

Project67Simpleharmonicmotion.Thespringpendulum 235

Project68Generatingsinewaves 238

Project69Naturalfrequency 241

Project70Bunsenburnerpipeorgan.Resonantfrequency 243

Project71Springsandelectromagnets.Resonance 246

Project72Speedofsound.Timinganechooldschool.WhyGalileocouldn’tdothiswithlight 248

Project73Speedofsound.Resonanceinacylinder 250

Project74Racingagainstsound.Dopplereffect 253

Project75Addingsounds.Beatfrequency 255

Project76Pendulumwaves 258

Project77Usingwavestomeasurethespeedofsound 261

Section7Light 266

Project78Rayoptics.Tracingthepathoflightusingalaser 266

Project79Twocandles,oneflame 274

Project80Laserobstaclecourse 277

Project81Lightintensity.Puttingdistancebetweenyourselfandasourceoflight 280

Project82Howdoweknowthatlightisawave?ThomasYoung’sdoubleslitexperimentwitha

diffractiongrating283

Project83Howtomeasurethesizeofalightwave 285

Project84Thespeedoflightinyourkitchen.Visitingthelocalhotspots 288

Project85Refraction.Howfastdoeslighttravelinairorwater? 291

Project86Polarization.Sunglassesandcalculatordisplays 294

Project87Whatisthewireofafiber-opticnetwork?Totalinternalreflectionusingalaseranda

tankofwater299

Project88Thedisappearingbeaker 303

Section8HotandCold 306

Project89HowmuchheatisneededtomeltGreenland?Heatoffusion 306

Project90Awaterthermometer 309

Project91Whatisthecoldestpossibletemperature?Estimatingabsolutezero 312

443

Project92Liquidnitrogen 316

Project93Boilingwaterinapapercup 320

Project94Boilingwaterwithice 322

Project95Seebeckeffect/Peltiereffect.Semiconductorheating 325

Section9ElectricityandMagnetism 328

Project96Staticcharges 328

Project97Makinglightning.ThevandeGraaffgenerator 333

Project98TheWimshurstmachine.Separatingandstoringcharges 338

Project99Runningintoresistance.Ohm’slaw 341

Project100Circuits:Bulbsandbuzzers 344

Project101Howdoesheataffectresistance? 347

Project102Resistivity.Canironconductelectricitybetterthancopper? 349

Project103Storingcharge.Capacitors 352

Project104Isthemagneticforcemorepowerfulthangravity? 356

Project105Magneticlevitationusinginduction.Electromagneticringtosser 360

Project106Magneticlevitationusingsuperconductivity.TheMeissnereffect 363

Project107Movingelectronsproduceamagneticfield.Oersted’sexperiment.Themagneticfield

ofacurrent-carryingwire367

Project108Faraday’sexperiment.Currentgeneratedbyamagnet 369

Project109Ifcopperisnotmagnetic,howcanitaffectafallingmagnet?Lenz’slaw 371

Project110Effectofamagnetonanelectronbeam.Theright-handruleformagneticforce 375

Project111Whatistheshapeofamagneticfield? 378

Project112Whathappenstoacurrent-carryingwireinamagneticfield? 380

Project113Ano-frillsmotor 382

Project114Magneticaccelerator 385

Project115Alternatingcurrent 387

Project116Thediode.Anelectronicone-wayvalve 391

Section10TheEarth 394

Project117MeasuringtheEarth’smagneticfield 394

Project118WeighingtheEarth 399

Section11TheTwentiethCentury 402

Project119Whatisthesizeofaphoton? 402

Project120HowisahydrogenatomliketheNewJerseyTurnpike?Seeingtheenergylevelsof

theBohratom405

Project121Photoelectriceffect 408

Project122Millikanoil-dropexperiment.Mysterymarbles.Understandinghowtheexperiment412

444

worked 412

Project123Ping-pongballchainreaction 415

Project124Thesodiumdoublet.Whydowethinktheelectronhasbothupanddownspins? 418

Project125Buildingacloudchamber.Whymuonsshouldnotbehere.Specialrelativity 420

AppendixA 426

AppendixB 427

Index 432

445