L e s s o n P l a n : F o r c e

Background

Forceisapushorapullonanobject.Pushingorpullingfasterincreasestheforce.Forexample,forceisproducedonaballwhenyouthrowitintotheair.Thefasteryouthrowit,themoreitsacceleration,orrateofchangeinvelocityovertime,increases,andtheforceproducedontheballincreases.Newton’sSecondLawofMotion,F=ma,wherem=mass(kg)anda=acceleration(meter/sec2),accountsformanyoftheforcesunderlyingactionsinoureverydaylife.Animportantforcethataffectseveryoneonearthisgravity.Theaccelerationduetogravity(theainF=ma)isessentiallyconstantforallobjectsonEarth.Thisistrueintheabsenceoffriction,ordragforce,whichactstoopposethemotion.Theeffectsofgravitationalforcehaveconfusedhumanssinceancienttimes.TheGreekphilosopher,Aristotle,thoughtthatgravityactingontwoobjectsofdifferentmasseswouldcausethemtofallagivendistancetoEarthatdifferentspeeds.Accordingtolegend,thegreatItalianscientistGalileoprovedthatthisideawaswrongbydroppingtwocannonballsofdifferentmassesfromtheLeaningTowerofPisa.Theballslandedatthesametime,leadingGalileotoconcludethatobjectsfalltoEarthatthesamevelocity,contradictingAristotle’steaching.ThefindingthatthetimerequiredforthetwoballstofalltoEarthisthesamemeansthatthevelocityofthetwoballsisthesame.This,inturn,impliesthattheaccelerationduetogravity,orrateofchangeinvelocityovertime,a=Dv/Dt,isthesameforthetwoballs.Thisisalsotrueforotherobjects,disregardingdragforce–allobjectsfallwiththesamevelocityandlandatthesametime,sincetheaccelerationduetogravityisessentiallyconstantforallobjectsonEarth.Forexample,ateenagerwhoweighs100lb(45.5kg)shouldhitthewateratthesametimeasachildof50lb(22.7kg)whentheyfreefallintoaswimmingpool.Includingdragforce,thetimesmayvaryslightly.ThislaboratoryprovidesademonstrationofNewton’sSecondLaw,F=ma,byshowingthattwoobjectsthatdifferinmasslandatthesametimewhendroppedfromthesameheight.Theobjectslandatthesametimebecausetheiraccelerationduetogravity,a=9.8m/s2,isthesame.Objectives&GradeLevel

Demonstratetherelationshipbetweenfallingtimeandvelocity.Illustratetheeffectsofgravityonobjectsofthesameordifferentmass.Appropriateforearlytoadvancedhighschoolscienceclasses.Materials&Equipment

• Twoballsofthesamesize,butdifferentmasses(oneisheavierthantheother)• Twoballsofthesamesizeandthesamemass• Twoapplesthataresimilarinsize,butdifferinmass(oneisheavierthantheother)• Meterstick• Plumbline

Asimpleplumblinecanbemadefromastringandaweight• Camera(e.g.,cellphonecamera)• Calculator

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• BalanceorscaletoweighballsandapplesApostagescaleorkitchenbalancecanbeused

• Notebookandpencilforrecordingdataandmakingcalculations

Procedure

Experiment1:Twoballsofthesamesizebutdifferentmasses

Objective:Demonstratethatthefallingtimeisthesamefortwoballsofdifferentmasses.Theforceofgravityactingonthetwoballsisthesame,causingthemtofallatthesamevelocityandlandatthesametime.

1.Weigheachoftheballsonabalancetoobtaintheirmass.Recordthemassofeachballinthedatatablebelow.Scientistsusekilogramsastheunitofmass.Ifyourbalanceiscalibratedinounces,convertouncestokilogramsusingtherelationship1oz=0.0283kg.Ifyourbalanceiscalibratedinpounds,convertpoundstokilogramsusingtherelationship1lb=0.454kg.TwoballsofthesamesizebutdifferentmassesareshowninFig.1.2.Standingonafloororlevelsurface,measureaheightof1meter(m)fromthesurfaceusingameterstick.Makesurethemeterstickisstraightandnottilted.Confirmthisbyholdingaplumblinenexttothemeterstick(Fig.2).Ifyouareusingayardstickinsteadofameterstick,convertinchestometersusingtherelationship12in=1ft=0.305m.Note:Aplumblineisusedtofindalineperpendiculartoasurfaceusinggravity.Aplumblinecanbemadeusingastringandasmallweight,suchasafewwashers.Whydoeshavingalevelsurfaceandaplumblinematter?3.Holdthetwoballsataheightof1m.Haveafriendreadytorecordavideoofeachtrialwithacellphonecamera.4.Dropbothballsfromthesame1-meterheightandmeasurethetimeincentiseconds(cs,acentisecondisonehundredthofasecond)thatittakesforeachballtohittheground.Recordeachtrialusingacellphonecamera.Besurethatyoureleasetheballsatthesametimewithoutforce.Tryafewpracticedropsbeforestartingtheexperimenttomakesurethatbothballsarereleasedatthesametimefromthesameheight.Lookatthevideorecording,frame-by-frame,tomakecertainthattheballswerereleasedatthesametime.Iftheballswerereleasedatslightlydifferenttimes,determinethetimerequiredforeachballtotouchthegroundseparately,ratherthanusingthesamestartingtimeforbothballs.5.RepeatStep4sothatyouhave3-5trialsinall,recordingthetimesandfilmingeachtrial.Besurethatyouconfirmthestartingandendingtimesfromthetimestampsontheindividualframesinthemovies.Recordtothenearesthundredthofasecond(theseconddecimalplace,0.00s).6.Findtheaveragetimeforallthetrialsforeachballusingacalculator.UsetheLessonPlanonExperimentalErrortodeterminetheexperimentalerrorforallthetrlalsforeachball,e.g.,themean±sd(mean±standarddeviation).Comparethemean±2sdforeachballtodetermineiftheballsshowdifferencesintheirfallingtimes.Ifthe

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mean±2sdforthefallingtimesofthetwoballsoverlap,thedifferencesareprobablyduetoexperimentalerrorinthetrials,e.g.,releasingtheballsatslightlydifferenttimesornotidentifyingthecorrecttimethattheballswerereleasedorhittheground.Ifthemean±2sdforthetwoballsdonotoverlap,thedifferencesareduetoactualdifferencesinthefallingtimesofthetwoballs.Whydidwedotheexperimentatleastthreetimesandwhydoweneedtotaketheaverage?Istheaveragetimethattheballstooktohitthegroundthesameordifferent?Viewthevideosofthetrialstoconfirmyouranswer.7.Usingtheformulav=at,calculatethevelocityofeachball.Rememberthattheaccelerationoftheballsduetogravityisa=9.8m/s2.Again,calculatetheexperimentalerrorforthevelocityofeachballtoseeifanydifferencesinyourresultsareduetoexperimentalerrororactualdifferencesinthevelocitiesoftheballs.Isthevelocityoftheballsthesameordifferent?

Experiment2:Twoballsofthesamesizeandmass

Objective:Thisisacontroltoshowthattheaccelerationduetogravityisthesamefortwoballsofthesamesizeandthesamemass.Theballsshouldlandatthesametimeandwiththesamevelocity.

1. RepeatSteps1-6fromExperiment1andrecordthedata.UsethesedataandwhatyouhavelearnedfromExperiment1topredictthevelocitiesofthetwoballs.

2. Usingtheformulav=at,calculatethevelocitiesoftheballs.Didtheballsfallwiththesamevelocity?

Experiment3:Twoapplesofsimilarsizebutdifferentmasses

Objective:UsingwhatyoulearnedfromExperiments1and2,predicttheresults;thenperformthetrialsandcalculatethevelocityofeachapple.

1. RepeatSteps1-6fromExperiment1andrecordthedata.Usethesedataandwhatyouhavelearnedfrom

Experiments1and2topredictthevelocitiesofthetwoapples.

2. Usingtheformulav=at,calculatethevelocitiesoftheapples.

3. Compareyouranswerswiththoseofyourfriends.

Doyouranswersmatchthoseofyourfriends?Didtheapplesfallwiththesamevelocity?

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DataTables

Experiment1:Twoballsofthesamesizebutdifferentmasses Mass(kg)Ball1_________

Time(s)Ball1

Time(s)Ball2

Ball2__________Trial1

Trial2

Trial3

Trial4

AverageTime(s)

Velocity,v=a t(m/s)

Experiment2:TwoballsofthesamesizeandmassMass(kg)Ball1_________

Time(s)Ball1

Time(s)Ball2

Ball2__________Trial1

Trial2

Trial3

Trial4

AverageTime(s)

Velocity,v=a t(m/s)

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Experiment3:TwoapplesofsimilarsizebutdifferentmassesMass(kg)Apple1_________

Time(s)Apple1

Time(s)Apple2

Apple2__________Trial1

Trial2

Trial3

Trial4

AverageTime(s)

Velocity,v=a t(m/s)

DiscussionQuestions

1. ______________(Height,Mass,Size)determineshowfastanobjecthitstheground(i.e.,determinesthevelocity).

2. Newton’sSecondLawofMotionstatesthattheaccelerationofobjectsduetogravityis________m/s2.

3. Objectsofdifferentmassesfallingfromthesameheighthitthegroundat__________(thesame,different)time(s).

4. Theformulaforthevelocityofafree-fallingobjectis____________.

Figures

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Fig.1Twoballsofthesamesizebutdifferentmasses

Fig.2PlumbLine

Aplumbline,madefromapieceofstringandaweight.Onemeterwasmeasuredfromthefloorusingtheplumblinesothemeasureddistancewasverticaltothefloor.

The two balls are thesame size, but differ inmass. The mass of thehockey ball on the right(161.83 g) is ~1.65 timesthe mass of the baseballontheleft(98.34g).

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Fig.3Experiment1:Twoballsofthesamesizebutdifferentmasses.Theballsweredroppedfroma1-meterheightatthesametimeandrecordedwithacellphonecamera.Theimagesarestillsfromthemovie,whichwasrecordedat30frames/s.Theballshittheflooratthesametime,0.43saftertheywerereleased.Timeisshownas00:00=seconds:centiseconds.

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Experiment1:Twoballsofthesamesizebutdifferentmasses Mass(kg)Baseball98.34g=0.09834kg

Time(s)Baseball

Time(s)Hockeyball

Hockeyball161.83g=0.16183kgTrial1

0.43

0.43

Trial2

0.40

0.43

Trial3

0.40

0.42

Trial4

0.42

0.42

AverageTime(mean±sd,s)

0.41±0.02s

0.425±0.006s

Velocity,v=a t(m/s)

4.04±0.15m/s

4.17±0.06m/s

Methods:Experiment1wasperformed4timesandeachtrialwasrecordedwithacellphonecameraat30frames/s.ThemovieswereopenedinQuickTimePlayer7andthestartingframewasfoundbydraggingthecursortotheframeshowingthereleaseoftheballs,thenclickingonthetimewindow(00:00:00)andselectingFrameNumbertodisplaytheframenumber.Theendingframewhentheballshitthefloorwasfoundinthesamewayandthetime(s)wasdeterminedbysubtractingthestartingframefromtheendingframe,anddividingby30frames/s.Theaveragetimeandstandarddeviation(sd)weredeterminedusingGraphPadathttps://www.graphpad.com/quickcalcs/CImean1.cfm(seeBASICS:LessonPlanonExperimentalError).Conclusions:Themeantimes,plusorminustwicethestandarddeviation(baseball,mean±sd=0.41±0.02s,mean±2sd=0.37-0.45s;hockeyball,mean±sd=0.425±0.006s,mean±2sd=0.413-0.437s),foreachballtofalltotheflooroverlapwitheachother,indicatingthatthemeasuredtimesprobablydonotdiffersignificantlyfromoneanother–thedifferencesaremostlikelydueinsteadtoexperimentalerror(e.g.,errorsinreleasingtheballsatthesametimeordeterminingthestartingorendingtimefortheballsfallingtothefloor).Thisisalsotrueoftheoverlappingmean±2sdforthevelocitiesoftheballs.TheprobableabsenceofsignificantdifferencesforthefallingtimeandvelocitywasconfirmedusingGraphPadunpairedstatisticalttests,whichshowednosignificantdifferencesforthefallingtimesorvelocitiesofthetwoballs.Thismeansthatthetwoballsfallwiththesametimeandvelocity,despitethedifferenceintheirmasses.

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Acknowledgements

WethankBrentHoffman,HaroldEricksonandShawnHJeforhelpfulcommentsthatwereusedinwritingthisLessonPlan.ThislessonplanisbaseduponworksupportedbytheNationalScienceFoundationunderGrantNumberCMMI1660924.Anyopinions,findings,andconclusionsorrecommendationsexpressedinthislessonplanarethoseoftheauthorsanddonotnecessarilyreflecttheviewsoftheNationalScienceFoundation.

Authors

SharynAEndowArthiSKozhumamDukeUniversityMedicalCenterDurham,NC061518

Copyright©2018byBiophysicalSociety.Allrightsreserved.