PHYSICSPROJECTLABPhysics Project LabPaul GluckJerusalem College of EngineeringJohn KingMassachusetts Institute of Technology33Great Clarendon Street, Oxford, OX2 6DP,United KingdomOxford University Press is a department of the University of Oxford.It furthers the Universitys objective of excellence in research, scholarship,and education by publishing worldwide. Oxford is a registered trade mark ofOxford University Press in the UK and in certain other countries Paul Gluck and John King 2015The moral rights of the authors have been assertedFirst Edition published in 2015Impression: 1All rights reserved. No part of this publication may be reproduced, stored ina retrieval system, or transmitted, in any form or by any means, without theprior permission in writing of Oxford University Press, or as expressly permittedby law, by licence or under terms agreed with the appropriate reprographicsrights organization. Enquiries concerning reproduction outside the scope of theabove should be sent to the Rights Department, Oxford University Press, at theaddress aboveYou must not circulate this work in any other formand you must impose this same condition on any acquirerPublished in the United States of America by Oxford University Press198 Madison Avenue, New York, NY 10016, United States of AmericaBritish Library Cataloguing in Publication DataData availableLibrary of Congress Control Number: 2014940248ISBN 9780198704577 (hbk.)ISBN 9780198704584 (pbk.)Printed and bound byCPI Group (UK) Ltd, Croydon, CR0 4YYLinks to third party websites are provided by Oxford in good faith andfor information only. Oxford disclaims any responsibility for the materialscontained in any third party website referenced in this work.This book is dedicated to the memory of my co-author Professor John King,a great physicist and educator and a ne, warm, human being.Paul GluckAcknowledgmentsWe are very grateful to Professors Charles Holbrow and Gabriel Spalding for their critical reading of the manuscript andmaking extremely useful suggestions which we adopted in the revised version.Special thanks are due to Jessica White, Victoria Mortimer, and Richard Hutchinson at Oxford University Press for allthe help and kindness extended to us throughout the process of publication.ContentsFigure acknowledgments xProjects: why and how? 1Part 1 Mechanics1 Bouncing balls 132 Mechanics of soft springs 173 Pulse speed in falling dominoes 254 A variable mass oscillator 285 Rotating vertical chain 346 Cycloidal paths 387 Physics of rubber bands and cords 448 Oscillation modes of a rod 49Part 2 Electromagnetism9 Physics of incandescent lamps 5710 Propulsion with a solenoid 6211 Magnetic dipoles 6912 The jumping ring of Elihu Thomson 7413 Microwaves in dielectrics I 8014 Microwaves in dielectrics II 8615 The Doppler effect 8916 Noise 9417 Johnson noise 10218 Network analogue for lattice dynamics 10619 Resistance networks 111viii ContentsPart 3 Acoustics20 Vibrating wires and strings 11721 Physics with loudspeakers 12422 Physics of the tuning fork 12923 Acoustic resonance in pipes 13424 Acoustic cavity resonators and lters 13825 Room acoustics 14126 Musical instruments: the violin 14627 Musical instruments: the guitar 15128 Brass musical instruments 155Part 4 Liquids29 Sound from gas bubbles in a liquid 16330 Shape and path of air bubbles in a liquid 16831 Ink diffusion in water 17332 Refractive index gradients 17633 Light scattering by surface ripples 18034 Diffraction of light by ultrasonic waves in liquids 18435 The circular hydraulic jump 18836 Vortex physics 19237 Plastic bottle oscillator 19738 Salt water oscillator 201Part 5 Optics39 Birefringence in cellulose tapes 20740 Barrier penetration 21241 Reection and transmission of light 21542 Polarization by transmission 22143 Laser speckle 226Contents ix44 Light scattering from suspensions 23245 Light intensity from a line source 23646 Light interference in reecting tubes 239Part 6 Temperature and Heat47 Cooling I 24548 Cooling II 24849 The Leidenfrost effect I 25450 The Leidenfrost effect II: drop oscillations 25851 The drinking bird 26052 Liquidvapor equilibrium 26653 Solar radiation ux 270Appendix A: Project ideas 273Appendix B: Facilities, materials, devices, and instruments 290Appendix C: Reference library 310Index 315Figure acknowledgmentsExplanation of gure acknowledgments:4.4, 4.5: 71, 721(2003) means Figures 4.4 and 4.5 in the text, followed by the journal reference (volume number, pagenumber, publication year).Figures in the text reproduced with permission fromjournals published by the American Institute of Physics, by permissionof the American Association of Physics Teachers:American Journal of Physics:4.4, 4.5: 71, 721(2003); 11.4: 62, 702(1994); 13.2: 48, 648(1980); 13.4: 54, 712(1986); 13.5: 52, 214(1984); 14.2:45, 88(1977); 20.2: 53, 479(1985); 35.3: 67, 723(1999); 36.2, 36.4: 75, 1092(2007); 37.5: 75, 893(2007); 39.4: 41,1184(1973); 40.3: 43, 107(1975); 41.4: 50, 158(1982); 45.2: 63, 47(1995); 48.2: 61, 568(1993); 52.2: 64, 1165(1996).The Physics Teacher:9.2: 45, 466(2008); 23.2, 23.3: 44, 10(2006).Physics of Fluids A:30.2: 14, L49(2002).Figures in the text reproduced from journals published by the Institute of Physics UK, by permission of IOP Publishing:Physics Education:1.4: 33, 174(1998); 1.5: 33, 236(1998); 2.9: 45, 178(2010); 6.66.11: 45, 176(2010); 10.3, 10.4, 10.9: 45, 466(2008);12.7: 7, 238(1972); 28.1, 28.2, 28.3: 38, 300(2003).European Journal of Physics:18.7: 1, 129(1980); 29.3, 29.4: 8, 98(1987); 21, 571(2000); 44.3: 7, 259(1986); 46.3: 13, 47(1992); 48.3, 48.4, 48.5: 30,559(2009).Projects: why and how?Introduction 1What is a project? 2Overcoming the fear 4Tools of the trade 5Researchers, choices, and the toil 7Is it worth the effort? 9About the book 9IntroductionThis book is intended for our colleagues, teachers of physics at universities andcolleges, and their students. While signicant reference is made to material typic-ally encountered beyond the rst year of university-level study, high school teachersand their students may also nd many opportunities here. Like us, many readershaveprobablybeenteachingphysicsmostoftheirlivesinwhatmaybecalledtransmission mode, that is, instruction by means of textbooklessonrecitationlaboratory.Inthismodewe,theteachers,send,andourcharges,thestudents,receiveinformationandskills,inconformitywithJohnLockesnotionthatthestudents mind resembles an empty slate to be written on.But there is another mode of instruction, exemplied by what Rousseau wrotein his book Emile: Teach by doing whenever you can, and only fall back on wordswhen doing is out of the question. We may call this the transformation mode.Now, both teacher and student are transformed into explorers, with benets toboth. Fortheteachersinaresearch-basedinstitutionnothingshouldbemorenatural than to carry over the research style into some of their teaching activity.Why this does not happen more often deserves serious discussion. For teachers ina high school it is an opportunity to partake in and guide research, and this couldprove to be the activity that relieves repetition and lifts them from the rut. For thestudent it is a chance to experience the way science works.An important aspect of the project lab is that the teacher, though generally ex-perienced, doesnt always know the answers to the questions raised in the projectany more than the students do. So much so that instead of the words teacher andstudent we will use guide and researcher. (Except when we quote.)The two modes of learning should be combined in a proportion that suits thepersonalities of guides and researchers alike. It is not our aim in this book to evalu-ate the competing modes. The research literature in physics teaching in the past30 years has been devoted to that, and it behooves us to be mindful of it. Rather,we should like to extend an invitation to the reader to try something different, atleast as far as laboratory work is concerned, namely, to teach physics by guidingresearchers through projects. It may happen that once tried, the experience willbe habitforming, and thatshall be ourreward forwriting thisbook.For thoseof our readers who have guided projects for years these remarks are like preach-ing to the converted. We hope that for them this book will be a source of furtherideas.2 Physics Project LabWhat is a project?GregLockett, ateacherwhoparticipatedintheLabNetprojecthasdescribedimportant aspects of project lab [1]:Thegoal of theguideistore-createtheprocessandexperienceofworking in the physics laboratory. Several features are important in thisapproach. Students are free to choose a research problem. They do notknow the solution to their problem at the outset. While they work withinthe constraint of time, resources and their current knowledge, they aregiven sufcient time and freedom to attack their problem as they see t.Collaborationisacceptableanddesirable.Theendproductcanvary:reports, papers, equipment, experiments, models, etc.In this process the goal is to give the student an immediate insideviewof howphysics is done. The teacher functions as a facilitator, some-what like a research director in a laboratory: obtains needed resourcesor suggests alternatives, resolves disputes about equipment schedul-ing and squabbles between partners, attempts to foster new ideas andtechniques, and strengthens theory when needed.Skills are learned as needed. These include guided journal, book andInternet searches, motor skills in building apparatus, social skills of col-laboration, communicationskills(oral, writing, optimal presentation),andmathematicalandanalyticalskills.Theprojectwilldemandthesenaturally, so problems of motivation will not arise.We would also like to quote two people involved in experimental physics whodescribe what we feel ought to be the approach to doing projects; namely, thatthe researcher should acquire the beginnings of various skills that were once es-sential inexperimental physics.Althoughinrecentdecadesdigital instrumentshave largely supplanted analog techniques, their inner workings are often not wellunderstood by the user. In spite of the value and importance of digital techniques,we think that beginner researchers would also benet from hands-on experiencewith earlier, understandable analog techniques.Here is what Nobel Prize winner P.M.S. Blackett had to say [2]:The experimental physicist is a jack-of-all-trades, a versatile but amateurcraftsman. He must blow glass and turn metal, though he could neitherearn his living as a glass-blower nor be classed as a skilled mechanic; hemust do carpentry, photograph, wire electric circuits and be a master ofgadgets of all kinds; he may nd invaluable a training as an engineer andcan always prot by utilizing his gifts as a mathematician. In such ac-tivities he will be engaged for three-quarters of his working day. Duringtheresthemustbeaphysicist,thatis,hemustcultivateanintimacyProjects: why and how? 3with the behaviour of the physical world. Bur in none of these activities,taken alone, need he be pre-eminent, certainly neither as a craftsman,for he will seldom achieve more than an amateurs skill, nor even in hisknowledge of his own special eld of physics need he, or indeed perhapscanhe,surpasstheknowledgeofsometheoretician.Foratheoreticalphysicist has no long laboratory hours to keep him from study, and hemustingeneralbeaccreditedwithatleastanequalphysicalintuitionandcertainlyagreatermathematical skill.Theexperimental physicistmust be enough of a theorist to know what experiments are worth doingand enough of a craftsman to be able to do them. He is only pre-eminentin being able to do both.Inamoregeneral veinFrankOBrien, aseniorresearchtechnicianintheMITmolecularbeamlaboratory, andaguideovermanyyearstomorethan150 graduate and undergraduate researchers, has this to say [3]:Listen to honest advice with an open mind, have an ear that listens andcomprehends.Practiceingenuitywithsimplicity.Bepatientandcom-prehend what you observe. Know how to relax. Have a sense of humor.Havesomeabilitytorelatetopeople. Traintohaveasteadyhand.Be reasonably versed in sketching, drafting, machining, measuring ac-curately when needed, plumbing, circuit wiring, jewelry work, soldering,brazing, welding and trouble-shooting.A project is the experimental exploration of physical phenomena, coupled withsome understanding of the theory behind them. On the one hand, this denitionis exible enough to subsume the behavior of everyday objects and phenomena,and to cater for the curiosity and enthusiasm of any researcher or guide interestedin them. On the other hand, it is a commitment to measure, collect, classify, andanalyzedatainacontrolledmanner, andifpossibleunderstanditintermsofsome model or theory, and not to be satised with building gadgets or apparatus,however ingenious.Nowwheredoes oneget ideas for projects?For thecurious andtheob-servanttheyareeverywhere. Seeminglytrivial occurrencescanbeinvestigatedthoroughly, at increasing depths of sophistication, and may engage the attention ofresearcher and guide alike for time spans that go way beyond the initial estimate.We hope to demonstrate this for a number of cases in later chapters. Sometimesone can pair researchers with a common interest, as deduced from a simple ques-tionnaire; for instance, two string instrument players who would be interested inhow a bow excites and damps a string, or the acoustical effect of varnish on thewood. The underlying interest and enthusiasm in these cases is invaluable. Hereare a couple of examples, described in later chapters, to whet the appetite and tocalm readers who might panic, not knowing what subjects to offer to or acceptfrom their students.4 Physics Project LabWhat regularities are there in the time-dependence of the glug-glug empty-ing of a bottle turned upside down? What if two such bottles are connected: willthey empty in phase?Water from a tap hits a sink and a circle of liquid is formed there. What factorsinuence the radius of this circle?Indeed, thebehavior of anyobject under changingcircumstances, or anynatural phenomenon,revealsphysical propertieswhichcanbemeasured,theircorrelations explored, their behavior understood and therefore often controlled.There is usually more than meets the eye, and the uncovering of that is the stuffof which projects are made.Overcoming the fearIt canbealongpathfromdeningaproject toknowinghowtonavigateittoareasonablysatisfyingconclusion. Variousproblemswithinstrumentation,construction, getting data, mathematical analysis, etc., may arise, along with frus-trations and dead ends, all coped with by helpful and continual guideresearcherinteraction. Inevitably there is an element of uncertainty and adventure in all this,especiallyifthetopicdoesnotappearinabook, andhasnostandardanswerknown in advance.A certain condence is required in the process, in which the guide sometimeshas only the advantage of experience over the researcher. Condence can only beacquired by plunging in, not perhaps at the deep end but in the middle. By thiswe mean adapting existing experiments and investigations to the schools milieu.We hope that the material presented in this book will be helpful in this respect.The process may be likened to the comedian who begins by telling the jokes ofothers, or those scripted for him or her. As expertise and condence grows, andthe tools of the trade are acquired, the stage of stand-up comedy is reached, invarying degrees of dexterity.There is a large body of experimental papers in the teaching literature, in jour-nalsliketheAmericanJournal of Physics, Physics Education, andtheEuropeanJournal of Physics. Indeed, manyoftheprojectsdescribedherehavetheirori-gininadaptationofarticlesinthesejournals. Thereisenoughofaspectrumhere, bothinsubjectsandinlevel, toappeal toawiderangeofpeoplewish-ingtostart. For that veryreasonthelevels of theprojects describedinthisbook are uneven. The website of the International Young Physicists Tournament,, is also a good source for projects.Some of the tools to be acquired will be discussed in the following sections.These, incombinationwithexperience, will leadtoanimportant, yet some-what intangible, expertise: one of knowing ones limitations, what is doable andunderstandable with ones knowledge, equipment, budget, and time limitations.Acolleagueofourshasbeendoingprojectsforyears.Hehasseveraltimesopined that he will not suggest a topic to a researcher unless he knows in advanceProjects: why and how? 5howtosolveitall theway. Ofcoursethisguaranteessuccess. Nevertheless,wedonotinsistonadheringtothisamountofcertainty. Italmostdefeatsthepurpose, and diminishes the mystery and fun.Tools of the tradeThe scope and the sophistication of a project will naturally depend on expertise,equipment, manpower, and the ability and willingness to learn. Sealing wax andstring cannot go very far. Experience has taught us to look out for the following.Shaping materials and signalsKnowingwheretogettheservicesofamachineshopandacarpenterisveryuseful. Youshapemetal, plastics, glass, andwoodtomakeapparatusperformfunctions otherwiseout of reach. If youcandothis byyourselves, somuchthebetter. Thesamegoes for thevaluableservices of anelectronics techni-cian. Thisisnot tosaythat oneshouldnot at least beconversant withsomeof the more widespread electronic devices and their circuits, since the detectionof and manipulation of signals in the measuring process will invariably demandthis. One might be led into believing that the advent of data acquisition systemsensors (usuallyreferred toasMBL,anacronymformicrocomputer-based la-boratory) has obviated the necessity for such skills, and to a certain extent thisis so. Nevertheless, employing only these will restrict the scope of measurementstotheirregimeofoperatingcharacteristics,withoutahopeofexpandingoneshorizons in order to minimize noise, to match sensors and transducers, to shapeand amplify signals (every measurement can be converted to a voltage), reducedistortions, perform a series of functions in tandem, and so on. The electronicinstruments now available can perform many functions, but it is fair to say thatfewpeopleknowhowtheyworkinanydetail; thisneednotbeaproblem, solong as they do the job and can be calibrated. There is some advantage to usingsimple analog instruments (analog oscilloscopes, signal generators, multimeters,etc.), particularly for people who are just beginning. There may be mystery in theproject, but why have it also in the instruments?Hoarding the good stuffBudgets are usually tight, but there are some basics without which one is not inbusiness. Power supplies, signal generators, oscilloscopes, optical and electroniccomponents are among these. More of this will be discussed in Appendix B oninstrumentation.Butappetitecomeswiththeeatingand,asyougoalong,youlearnthatserendipityfavorsthosewhoareawareofneeds.Sokeepaneyeonequipment discarded by researchers in academic and industrial institutions, andkeep in touch with them for projects in schools one does not need, or even want,6 Physics Project Labthe last word in sophistication, and the tools of the previous generation, or the lastbut one, are just ne. Bureaucracy often dictates that equipment not be given toyou but only lent for a limited but often indenite period. Who cares?Know where electric motors are reconditioned, for there you will nd motorsof all sizes, cheap or free, and insulated wires of all diameters for making coils.Use DC motors as speed sensors. Look out for ampliers from audio equipment,microphones, loudspeakers from defunct radio and television receivers, magnetsaroundthemagnetroninmicrowaveovens,stepmotorsandfansfromjunkedcomputers the list is long. Never buy anything new without searching the weband eBay; the supply and choice there are immense.Projects are about andwithmaterials, soyouneedtolearnwhere yourareas stores are situated for lumber, building materials, metal, plastic, Plexiglas(Perspex), glass, pipes, hardware(ball bearings, nutsandbolts, fastenersandglues, electrical parts), andelectronicsparts. Themoreproject-crazyyoube-come, the more expert you will be in locating what you need, for needs multiplyas the horizon is extended. Be aware, and let your eyes roam in these stores, toknowwhatgadgetsandmaterialsarearoundandmightcomeinhandyinthefuture. More details are given in Appendix B.Reference materialOur researchers and we guides always have much to learn as we go along. Oftenaguideisnotanexpertintheparticulareldofphysicsneededforthepro-ject. Looking up or learning theory, physical constants, material parameters, andmechanical and electromagnetic data will be a constant need. Much can be foundon the web, but in our experience there is no substitute for rst-class texts andmonographs when one wants to learn about a topic in depth. A university or col-lege library will usually have the basic needs, but can one suggest a useful schoollibrary? At the end of this book we list some of the accessible books that we havefound useful. We suggest that sooner or later these should nd their way to theshelves of all readers of this book, together with handbooks and catalogs.Design, invention, and perseveranceWe have little to say on these necessities. The hope is that some of the researcherswill be more inventive than the guide (we all wish that our children and researchersturn out better than ourselves). We realize that necessity is the mother of inven-tion, but what if the latter is delayed beyond endurance? Discuss things with yourcolleagues,theymayhaveanidea.Thentherearetheexpertsintheireldsatthenearestcollegeoruniversity.Comingtothempreparedwithawell-denedproblem and situation, and an account of your failed attempt to solve it, can oftenelicit a sympathetic response and result in useful advice.Do not abandon an investigation at the rst serious obstacle this results ina feeling of letdown for all. We know, because we have done this and tasted theProjects: why and how? 7bitter pill of failure. Modify, branch out in another direction, ght, and persist.Something of value will turn up.Researchers, choices, and the toilWehaveemphasizedthat projectsarefor thebenet of bothguides andre-searchers. But thesituationisnot symmetric, theburdenof responsibilityforsteering the project falls on the instructor.PartnersThebesthopeisthatresearcherswill choosepartnersamongthemselves, butthe instructor may be called on to sort out difcult or pathological cases. As al-waysinthesematters, listen, beunderstanding, andtrytohelp. Thepairingof partners withparallel interests bymeans of a simple questionnaire oftenworks.Choosing a topicIf researchers have a topic that fascinates them, so much the better. Popular sub-jects are sports, music, ight, human perception. Some students come with a rmchoice in mind others seem not to have any idea. Sometimes giving examplesof past projects classied under mechanics, heat, sound, electromagnetism, light,atoms may inspire choice. But some of these may turn out to be so general, out-landish, orexpensivethat somefocusingandparingdownmaybenecessary,somenegotiatedsettlementachievedwhichstill leavestheembersoftheiren-thusiasm glowing, and the feeling that the idea was theirs. Preservation of suchmotivation will contribute to steadfastness and a better chance of success. Hereare two examples of negotiated reductions of aspirations.Aresearcherwantedtoworkontelemetryandrocket propulsion. Hen-ished up building a water rocket, rigged up a force probe to an analog to digital(A/D) interface to measure reaction at lift off, and devised an optical method formeasuring the maximum height reached.Another researcher was interested in interior lighting. This led to an investiga-tion of the dependence of incandescent bulb lifetime on voltage, with excursionsinto radiation and thermodynamics.Noteveryresearcherknowswhatto choose,norarealltheirchoicesviable.Inanycase, adeadlinemust beannouncedbywhichvacillationscometoanendandchoices, ortheobviouslackof ideas, areclear. That alsomeanstheguide must have a reservoir of ready-made suggestions, pet ideas that have beenwaiting for a suitable pair to explore. Past projects that have only come to partialfruitionandhavemuchpotential forfurtherdevelopmentmaywell beamongthese.8 Physics Project LabThe daily toilCarrying out a project requires many skills and aptitudes, for researcher and guidealike: planning, manual dexterity, building, mathematical analysis, verbal articu-lation, wonder, enthusiasm. One or more may be present to an insufcient degreein a particular person. For this reason too, working in pairs is necessary, wherebythe partners complement each other. In the periodic meetings with the researchersthe guide will soon diagnose deciencies in one or the others skills and suggestwaystoimprovethem.Amongourdrives,thattowardscompetenceisamajorone, and one of the yardsticks for success as the projects of the whole class pro-ceed, and a source of satisfaction for the guide, is a perceptible improvement insome area of competence for every researcher.Guidingprojectsdiffersinmanywaysfromgivingalecturecourse, andismore like tutoring graduate researchers. The following features characterized ourprograms, sharply differentiating them from the usual mode of instruction: anyproblemmutuallyagreeduponbyguideandresearchercouldbeinvestigated,noclear-cutnalanswerswereknowninadvance,workwasdoneinblocksofuninterrupted time, there was plenty of planning but no syllabus, there were ex-ercises to learn how to use equipment, there was time to think and discuss mattersoutside the laboratory.At the Massachusetts Institute of Technology (MIT), projects lasted a semes-ter,workinginscheduledweeklyafternoonsessionsofvehours.TheProjectLab course was offered in each of two semesters a year, and it ran for 30 yearsas ascheduledcourse. Some22 2students participatedineachsemester,accompanied by a guide and an assistant.At the Israel Academy of Sciences, a high school for the gifted, Project Lab hasbeen conducted for 20 years and is continuing. The weekly allotment was a two-lesson period a week, but lasted throughout the year, with the added advantageofaboardingschool,whichmeansthatresearcherscouldcomeandworkout-side scheduled hours, the lab would be open in the evening once or twice a week,and a lab assistant would be present. Two guides were assigned to some 20 re-searchers, each responsible for 57 projects, each benetting from the support ofan experienced and enthusiastic lab assistant.The time burden may be heavy, both for guides and researchers. If possible,the guide also needs to be available for consultation outside the time slot ofciallyallottedtotheprojects. Forcontinuityit isvital tohavealaboratoryassistantwho accompanies the projects year after year, is familiar with the equipment andmaterials available, and shares some of the qualities and skills that are required ofthe guides, namely, ingenuity, experience, broadness of knowledge, and interests.These may not always be present even with the best of teachers or researchers.Somekindofclosureforthewholeclassisnecessary.Thisincludesacare-fulwrite-upoftheproject.Inaddition,itisusefultohaveaprivatehearingofeach team, devoted to a summary and questioning by the guide and a colleague,maybe even in the presence of an external examiner, lasting say 2030 minutes.Projects: why and how? 9This may also serve as a preparation for a short lecture to be given, the audiencebeing the rest of the class and possibly some invited guests.Is it worth the effort?Thebenetstotheguidearemany.Thereisnobetterwaytogettoknowre-searchers than in guiding them in projects. For guides at high schools or collegeswhereresearchtimeisabsentorminimal, projectsareanideal waytogetre-freshed, extend our own knowledge and skills, and break the routine of lecturingto a class. We might well adopt some of the materials and ndings of a project inour daily teaching, thereby making it more alive and attractive. For guides activein research, guiding projects is an opportunity to share their skills and knowledge,alaudableandnecessarycommunityservice, withthesidebenetofpossiblerecruiting of future undergraduate or graduate research students.The researcher will gain independence and learn a little about how science isdone. She or he will achieve something that was the fruit of struggle and labor,and take some pride in it. It may also be an inuence in considering science as acareer, something we science teachers are surely interested in promoting.About the bookWedescribeprojectstosuit varioustastesandresourcesinhighschoolsandcolleges. Separate parts are devoted to mechanics, electricity, acoustics, liquids,optics, and heat. Appendix A contains a list of additional ideas for projects, with-out the details given in the rest of the chapters. Some of the suggested projectsmay contain several of the above-mentioned topics. Theoretical background andsummaries are given in those cases where we felt that they would not be readilyavailable, but we frequently refer readers to the original articles in the teachingjournalliteratureorbookswheremoredetailscanbefound.Discussionoftheoriginal articles between advisor and researcher is a vital part of the process.We hope that by suggesting goals and possibilities for each exploration we haveset the stage and expectations for the reader. Not all those listed need or can berealized within the time or with the equipment available. It may well be that guideand researcher will suggest their own modications and extensions, in which casewehopethattheywill informthelearningcommunityatlarge,forthebenetof all.Therewill oftenbealternativestothemethods, detectors, instrumentation,and data processing suggested in the section on experimental suggestions. Budgetconsiderations will no doubt play a role in dening standards of sophistication andaccuracy, but we have usually set these to a level commensurate with the equip-ment of undergraduate or high school laboratories. Some guides might well thinkthat there is much value in researchers building their own sensors, A/Dconverters,10 Physics Project Labcontrol circuits, or software for data analysis, depending on the expertise of thoseinvolved and the skills the guide wishes to nurture and develop for his charges.This is indeed a laudable aim and part of the philosophy of Project Lab: minim-ize mystery. But the universal presence of complex, sophisticated digital devicesinthelivesofresearchersmeansthatthereshouldbenobarriertousingsimi-lardevicesinprojects. Thereadyavailabilityof packagesfordataacquisitionand analysis, digital oscilloscopes with memory, fast Fourier transform programs(FFT), and spectrum analyzers has made the carrying out of fairly extensive ex-perimental investigations available to a wider audience, and many of the projectsin the book rely on such facilities.What follows aredescriptions of projects that havebeeninventedanddone,andareexamplesforthereader-guidetobuildonwithhisorherresearchers.AppendixBshouldhelpinprovidingmaterialsandsettingupfacilities, somenecessary at the start, some that evolve with each session.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .REFERENCES1. G. Lockett, inLabNet: TowardaCommunityof Practice, R. Ruopp(ed.)(Erlbaum Associates, Hillsdale, NJ, 1993), p. 351.2. P.M.S. Blackett, The craft of experimental physics, in University Studies, H.Wright (ed.) (Nicholson & Watson, London, 1933).3. F. OBrien, private communication.Part 1Mechanics1 Bouncing balls 132 Mechanics of soft springs 173 Pulse speed in falling dominoes 254 A variable mass oscillator 285 Rotating vertical chain 346 Cycloidal paths 387 Physics of rubber bands and cords 448 Oscillation modes of a rod 49Bouncing balls1Introduction 13Theoretical ideas 13Goals and possibilities 14Experimental suggestions 15IntroductionBouncing plastic or rubber balls inated to different pressures present the experi-menter with an array of parameters, and it is a challenge to be able to isolate oneor the other in a controlled manner in order to measure its inuence on what hap-pens in a bounce. Interesting effects can also be investigated when non-inatableballs (ball bearing, baseball, golf, super, or tennis balls) are dropped on varioussurfaces, such as granite, steel, or wood. Among these are coefcients of restitu-tion, static and dynamic hysteresis curves related to energy losses, and the timeand distance dependence of the ballsurface interaction.Theoretical ideasInatable ballsAfterrstcontactwiththesurfacetheball continuestomovedownacertaindistortion distance d, before coming to a stop and rebounding. Energy and mo-mentum considerations enable one to estimate, for a given drop height h, both dand the average force Fof the surface on the ball, the timefor which the ballremains in contact with the surface, and the deceleration after contact. Since boththeareaofcontactSformaximumcompressionand canbemeasured,itisnatural to ask how depends on impact speed, and how S and depend on h, onthe excess pressure P in the ball, and on the radius of the ball R.A very crude model for the distortion can give some guidelines and a pointof departure for comparison with measurements [1]. If one neglects the stiffnessof the balls material, the contact force is S times P in equilibrium. The simplestassumption for S is to assume that the rest of the ball retains its spherical shape butthat the bottomforms a circle of radius a, as in Fig. 1.1abRFigure 1.1Ball model.. Then d = R b, a2 2Rd(for dsmall, d