sample lab report2013

7/30/2019 Sample Lab Report2013

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TheEfficiencyofaSuperBall

Background

Inthislabourpurposewastodeterminetheefficiencyofasuperball

asitisdroppedfromdifferentheights.Efficiencyistheratioofenergyouttoenergyin.Whenaballstrikestheground,itdoesso

withacertainamountofkineticenergyduetoitsspeed.Duringthe

bounce,theballdeformsasthekineticenergyisconvertedinto

elasticenergy.Astheballrebounds,theelasticenergyisreturnedto

kineticenergy.Thisprocessisnotperfect,however,andheatenergy

isgeneratedasmoleculesarepushedagainsteachother.Also

energyislosttothefloorandtotheairasvibrationsandsound.If

theballreboundswith90%ofthekineticenergythatithadbefore

theimpactthenwesayithasanefficiencyof90%.Itispossiblethat

theballsefficiencyisnotconstant;thatwhenitisdroppedfromahighheight,landingwithgreatspeeds,itismoreorlessefficient

thanwhenatlowerenergies.Ouranswer,thereforemaynotbea

singlenumber,butinsteaditmightbeafunctionofhowefficiency

variesoverdropheights.

Wemakeseveralassumptionsinthislab:weassumethatair

resistanceisnegligibleandthereforethattheentireamountof

potentialenergy(mgh)thattheballhasduetoitsdropheightis

convertedintokineticenergy( m .( m and )

Wealsoassumethattheallkineticenergyafterthebouncereturns

topotentialenergyastheballslowsandreachesitsnewbounce

height.

Toanswerthequestionposedinthislabwewillcomparetheheights

fromwhichwedroptheball,totheheightstowhichitrebounds.

Sincethekineticenergythattheballhasimmediatelybeforeand

aftertheimpactareequaltothepotentialenergythattheballhasat

itshighpointsbeforeandafterthedrop(duetoourassumptionof

nosignificantairresistance)andsincetheheightoftheballisdirecty

proportionaltoitspotentialenergy,wecandeterminetheballsefficiencybytheratiooffinalheight/startingheight.

Efficiency=

Bygraphingtheefficiencyvs.thestartingheightwewillbeableto

seehowthisefficiencydependsonheight.Wewillalsoshowhow

Purposeisestablished

Keyterms

defined(efficiency,etc,)in

thecontextwithwhich

theywillbeused.Not

standalonedefinitions.

Relevantbackground

informationisprovidedto

helpmakesenseofideas

andfutureconclusion.

Overviewofmethodand

howquestionwillbe

answered.

Frequentlyyouwillusea

drawingtohelpmake

yourideasmoreclear.

Youcanchooseyourown

titleaslongasitsrelevant.


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theefficiencydependsonimpactvelocitybygraphingitagainst

velocitytoo.

Methods

DataandCalculations

RawData

Starting

Height

(cm)

FinalHeights

(cm)

Trial1 Trial2 Trial3 Average

40 32 35 33 33.3

50 41 41 41 41

60 48 48 46 47.3

80 60 64 65 63

100 80 79 81 80

120 100 96 98 98

150 117 123 120 120

200 160 160 162 160.6

CalculatedValues

Starting

Height

(cm)

Efficiency

40 .83

50 .82

FinalHeight

hfinal

Wedroppedasuperballthreetimesfromeach

heightlistedonthedata

table.Eachtimewe

measuredthestarting

heightandthehighest

reboundpoint,basedon

thebottomoftheball.

Weusedameterstick

placedverticallyonthe

floorforourmeasurements.

Startingheight

hstarting

Clearlydefinedsections

tolabreport.

Keyvariablesclearly

shownonadiagram.

Nothingfancy,butifit

werecomplicatedit

mighttaketwodiagrams

oranexplanationofhow

togetameasurement.

Efficiency=

Noneedtoshow

samplecalculationsfor

simpleoperationsor

averaging.

Showrelevantformulas.

Units.

Clearlabelsoncolumns.

Alldatashown.Sometimesanumber

maybesooddthatyoudontwantto

includeitinyourcalculatedvalues,but

youshouldstillincludeitinyourtables.

Frequentlythedatatablesonloggerpro

getcutoff.Makesureyourdatatables

arecomplete.

Evenifyourereferencingsomeoneelses

graphs,youneeddatatables.


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60 .79

80 .79

100 .8

120 .82

150 .8

200 .8

Velocity

before

impact

(m/s)

Efficiency

2.8 .83

3.2 .82

3.5 .79

4.0 .79

4.5 .8

4.9 .82

5.5 .8

6.4 .8

Analysis

Thegraphofstartingheightvs.finalheightproducedfromthedata

clearlyshowsastraightlinefromtheorigin.Theslopeofthisgraph

0.807indicatestheratiooftheheightswhichwehaveshownis

equivalenttotheefficiency.Whileitscalculatedtothreedigitsof

V=

Samplecalculation

At40cm

V= =2.8m/s

Feelfreetoincludehand

writtencalculations.

ImnotincludinggraphsherebecausethisisasimpleworddocumentandIencourageyoutouse

LoggerProforyourgraphs.

Graphsshouldhavewelllabeledaxeswithunits.

Wheneverpossibledatapointsshouldhaveerrorbarsshowingyouruncertaintyaboutthedata

points.

Dottodotlinesareneverappropriate.

Insteadusetrendlines(sometimescurves).Includeequationsfortheselines.


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accuracy,thissurelyoverstatesouraccuracyasIwilldescribeinthe

nextsection.

Despitethisapparentlyveryclearresult,thereareseveralreasonstodoubtthisresult.

First,wemadetheassumptionthatnoenergywaslosttoair

resistance.Duringthebouncetheballmaybemoreefficientthan

80%andsomeofthislossmaybeduetoairresistance.However,

uponreflection,Ithinkignoringairresistanceremainsagood

assumption.Ifairresistancewassignificantthenthehigherdrops

shouldhaveexperiencedagreaterpercentageofenergyloss.That

theydidnt,indicatesthatairresistancewasntimportantandthe

bounceefficiencyreallywas80%.(Orthattherewasabigcoincidenceaboutfactorsexactlycancelingout.)

Moreimportantly,weonlytestedalimitedrangeofheights.We

knowthateventuallyballsstopbouncing,meaningthatfromsome

tinydropheightnothinghappens,0%efficiency.Thisprobably

happenswhenthecompressionbetweenmoleculesduringthe

bounceisonthesameorderofmagnitudeastherandommotionof

themoleculesduetotheirtemperature.Wealsoknowthatgiven

enoughspeedasuperballwillbreakasthecompressionalforces

exceedtheintermolecularforces.Toimprovethisexperimentit

wouldbegoodtoexpandtherangeofdatacollectiontoinvestigate

thisnonlinearbehaviorandeachendofthedata.

Finally,while80%efficiencyisprobablyareasonablyaccurateresult,

numerousmeasurementlimitationspreventedusfromgettinga

moreaccurateanswer.Weestimatethatwecouldholdtheballat

ourestablisheddropheightwithin0.2cmofaccuracy.Ourbounce

heightmeasurementswerenotnearlyasgoodunfortunately.

Sometimesourthreewatcherswoulddisagreeonabounceheightby

upto3cm,andourmultipletrialsforonecasespanned6cm(150

cmdropheight).Weindicatedthisuncertaintywith3cmerrorbars

onourfinalheightdata.Since3cmrepresentsa3%uncertaintyin

ourmediandropheightof100cm,wedecidedthatourfinal

efficiencyvalueshada3%uncertaintyandputerrorbarsof0.03on

them.Thisprobablyoverrepresentstheuncertaintyofthelarge

dropsandunderrepresentstheuncertaintyofthesmalldrops,but

ourgraphingprogramhaslimitedfunctionalityforsettingerrorbar

Describeyourconfidencein

ageneralway.Idothisa

bitwiththefirstsentence,

andabitmorewiththe

last.

Supportyourclaimof

confidence,orlack

thereof,bydiscussingthe

strengthsandweaknesses

ofyourexperiment.A

rangeofpossible

approachesisgivenon

theassignmentsheet.

Atleasttwoaspectsofyour

erroranalysisshouldhavea

quantitativeelement.Here

Ivedescribedmyoriginal

uncertaintyquantitatively,the

sizeofmyerrorbars

quantitativelyandhowthe

originaluncertaintyaffected


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size.Italsoassumesthatthelargeuncertaintyinthebounceheight

makesirrelevantthesmalluncertaintyinthedropheight.

Ouractualcalculatedefficienciesareallwithin3%of81%,asseenin

thefactthatthelineofbestfitpassesthroughtheerrorbarsofallof

thepoints.Thisandthefactthatthegraphhasayinterceptof0,predictingthat0dropheightwouldnotbounce,addtoour

confidenceinourresultof813%fortheefficiencyofoursuperball

nomatteritsdropheight.

Conclusion

Asdiscussedearliertheefficiencyofthesuperballisapproximatelyaconstant80%,whichisshownbybothaconstantslopeontheheight

graphandaconstantefficiencyonthesecondgraph.Apparentlyno

mattertheamountofcompressionoftheballduringimpact,the

intermoleculardampeningandheatgenerationcausestheballto

loseabout20%ofitsenergy.Whilethisresultcouldbetestedfor

greaterprecisionandaccuracy,Iamquiteconfidentinthegeneral

outcome.

Summarizethedata.

Address/answerthequestion

explicitly.

Inthiscase,thedatasupported

theconclusionclearlyandina

straightforwardway.Itwould

havesoundedsillytobelaborit,

Whenappropriate,propose

atheoreticalexplanationfor

yourresults.

Errorpropagation(how

originalerrorsaffect

calculatedvalues)canbea

verycomplicatedthing.

Imalrightwithyour

makingsomesimplifying

generalitieslikeIhave

here.

Yourerroranalysispartis

whereyoucanreallyshow

offadeepunderstandingof

whatsrelevantinthelab.

Putsomethoughtintoit.

Showoff.

sample lab report2013

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