Lab2:Free-Fall
Physics203:ProfsMartensYaverbaum&Bean
JohnJayCollege,theCityUniversityofNewYork
INTRODUCTION
Howdoobjectsinfree-fallmove?Dotheymoveatasteady—constant—speed?Or
dotheygetfasterorslower(accelerate)astheyfall?Iftheydoacceleratedoesthe
rateofaccelerationstayconstant...ordoesthatchangetoo—inotherwords,does
theaccelerationgetbigger/smallerovertime?Andiftheaccelerationischanging
overtime,doesitkeepchangingatasteadyrate,oristhatratechangingtoo?Etc.
Inthisexperiment,wewilltrytoanswerthesequestions.
Inordertodoso,wewilldroplong,verticalstringswithmachinescrewsattachedat
variousintervalsalongthestringfromheightsof3-5metersandlistentothetiming
(rhythm)ofthescrewsastheyhitametaltrayatthebottomoftheirfall.
OBJECTIVES
InplainEnglish:
todeterminehowfallingobjectsmove.
Inmorecomplicated(butalsomoreprecise)English:
toanalyzethebehavioroffallingobjectsintermsofthederivatives(first,second,
etc.)ofpositionwithrespecttotime.
Anobjectissaidtobeinfree-falliftheonlyforceactinguponitisgravity.Anything
flyingthroughtheair,whetheritwasthrownordropped,isinfree-fall(aslongasit
doesnothavejet-packsorpropellers,andweignoreair-resistance).
WHATWEKNOW
• Thedefinitionsofdistance&displacement.
• Thedefinitionsofaveragespeed&averagevelocity.
WHATWEDON’TKNOW
Everythingelse.
PROCEDURE
A. CreatingandTestinganEvenly-SpacedString
1. Cutastringapproximately5metersinlength.
2. Witharulerandpencil,markoff5to10equallyspacedpositions.Thefirst
markshouldbeallthewayatoneendofthestring.(Withintherangeof5-10,
it'suptoyouhowmanypositionsyoumark.Themorepositions,themore
datapoints.Themoredatapoints,however,thelessclearlydistinguishable
theybecome.)
3. UsingSLIPKNOTS,attachamachinescrewateachofthemarked-off
positions.
4. Waitforallothergroupstocompletestep3.Whilewaiting,readahead.
5. Onceallgroupsareready,eachgroupwillgooneatatimeanddropits
spatiallysymmetricstringfromahighlocation(approximately5meters)
ontoacookiesheet.Allothergroupswillquietlywatch,listenandrecord.
6. Yourlabinstructorwillleadyoutothislocation.Atthislocation,wewill
conductourselvesinasingularlyquietandreservedandcarefulmanner.We
willotherwisebecreatingahazard.
7. Listencloselytothepatternofsoundsmadebythescrewsastheyslaminto
thecookiesheet.Withacellphoneorhand-helddigitalrecorder,record
them.Ifyouhaveslowmotiononyourrecordingdevice,useit.
B. AnalyzingDatafromtheEvenly-SpacedString.
1. Listentoyourrecordinganddiscusswhatyouhear.
Asagroup,writedownyouranswerstothefollowingquestions:
2. Whathappenstothebeats(soundsofthescrewsstrikingthecookie-sheet)
asthestringfalls?
3. Whathappenstothetimeintervalbetweeneachbeat,asthestringfalls?
4. Howfardidthescrewsfallinbetweenthefirstbeatandthesecond?Howfar
didtheyfallbetweenthesecondbeatandthethird?Thethirdandthe
fourth?Etc.
5. Giventhepatterninthedistancetraveledbetweenbeats(questionB.4)&the
patterninthetimeintervalbetweenbeats(questionB.3),whatmustbe
happeningtotheaveragespeedbetweeneachbeat,asthestringfalls?
C. SearchingfortheEvenly-TimedString
1. Cutanewstringapproximately5metersinlength.Eventually,thestringwill
beorientedVERTICALLYandsothatitsbottomendisquitenearthe
ground.Itwillbedroppedontoacookiesheetsothatthemachinescrews
makealoudnoiseuponcontact.
THE GOAL : attach the screws to the string in such a way that they
create a steady rhythm as they land. In other words, the time in
between the beats should stay the same as the string falls.
2. Withpencilandpaper,spendtimeCAREFULLYcontemplatingwhereonthe
stringyoubelievemachinescrewsoughttobeplacedinordertomeetThe
Challengedescribedabove.
Withoutactuallydroppinganystring,clearlywriteoutallyour
thoughts.Theymaybewords,numbers,equations,etc.NOTHOUGHTS,
however,mayultimatelybeusedwithoutspecificjustification.Anisolated
equationthatyoumayhaveseenormemorizedisNOTitselfajustification.
Tohelpyoudeviseyourmethod,gobacktotherecordingyoumadeofthe
evenly-spacedstringdrop.Whatmustyoudoinordertomakethetime
intervalsequal?
Oneofthethingswetendtoassumeabouttheworldinphysicsisthatitis
fullofmathematicalpatterns.Thatmightbeagoodthingtokeepthatin
mindwhendesigningyourstring.
3. Whenyouhavearrivedatacleardecision,beforeyoudoanytesting,you
mustdrawTWOdiagramstoshowyourpatternofscrewplacements:wecall
thesetheintervaldiagramandthepositiondiagram.
TheIntervalDiagramshowsthedistancesBETWEENthescrews.
ThePositionDiagramshowsthetotaldistancefromeachscrewtothe
bottomofthestring.
Tohelpyougetthehangofposition&intervaldiagrams,trythetwo
exercisesbelow.
Exercise1:belowisapositiondiagramofastringwith5screwsonit.
Convertthisintoanintervaldiagram.
300cm 280cm
TopofString
240cm
160cm
0cm
Bottomof
String
Exercise2:belowisanintervaldiagramofastringwith7screwsonit.
Convertthisintoapositiondiagram.
60cm
60cm
60cm
60cm
60cm
60cm
Bottomof
String
TopofString
4. Afteryouhavecomeupwithyourplanforyourevenly-timedstringand
created,showyourwork(includingbothapositionandanintervaldiagram)
toyourlabinstructor.
5. Onceyourthoughtprocessisapprovedbyyourinstructor,usetherulerand
penciltomarkoffthepositionsonyoursecondstring.
6. Usingslipknots,attachscrewstoallmarkedpositionsonyourstrings.
7. Withextremecaution,wrapyourstringaroundyourforearmsothatit
becomesatight,un-knotted,portablepackage(notatangledmesswith
screwsfallingoffofit).
8. Usemaskingtapeandpentolabelyourstringwiththenamesofyouand
yourpartner.
9. Ontoacookiesheet,fromthesamelocationasbefore,dropyourtemporally
symmetricstringfromahighlocation(approximately5meters).
10. Listencloselytothepatternofsoundsmadebythescrewsastheyslaminto
thecookiesheet.Recordthem.
11. Didyouachieveansteadyrhythm?Ifnot,gobacktothedrawingboardand
makeanewplan.
12. Beforethelabisover,yourinstructorwillaskyoutocreatetwostringsbased
onmathematicalpatterns.WewillcallthesepatternspatternAandpattern
B.Youwillfindoutwhattheyareduringthecourseofthelab.
D. MathematicalAnalysisofPatterns.
1. ForPatternA:
a. Drawapositiondiagram.Makesuretoincludeatleast6screws.
b. Belowthepositiondiagram,writedownthedistancesbetween
screws(i.e.theintervals).
c. Belowthedistances,writedownthedifferencesbetweenthe
distances.
d. Belowthedifferencesbetweendistances,writedownthedifferences
betweenthedifferencesbetweendistances.
e. Whatdoyounotice?
Yourworkwilllooksomethinglikethis:
Position Position Position Position Position Position
ofBoltF ofBoltE ofBoltD ofBoltC ofBoltB ofBoltA
Dist.5
Dist.4
Diff.4
Dist.3
Diff.3
(it’sokifyoucan’tmakethosecoollittle
Dist.2
Diff.2
Dist.1
Diff.1
shapes.)
2. ForpatternB:
a. Drawapositiondiagram.Makesuretoincludeatleast6screws.
b. Belowthepositiondiagram,writedownthedistancesbetween
screws(i.e.theintervals).
c. Belowthedistances,writedownthedifferencesbetweenthe
distances.
d. Belowthedifferencesbetweendistances,writedownthedifferences
betweenthedifferencesbetweendistances.
e. Whatdoyounotice?
3. Nowtrythissametypeofanalysisforatypeofpatternthatcomesupalotin
bothscienceandmathematics:anexponentialpattern.Usethesimplest
exponentialpattern:1,2,4,8,16,32,etc.Followthesamestepsa.,b.,c.,d.,
etc.thatyouusedfortheothertwopatterns,andkeepgoinguntilyousee
howthispatternisdifferentfromtheothertwo.Willthisprocesseverend?
E. DrawingConclusionsaboutMotioninFree-Fall.
Wewillassumefromhereonoutthatoneofthepatternsyoutestedproduceda
fairlysteadyrhythm.(Ifyoudidnotfindanypatternthatproducedafairly
steadyrhythm,checkinwithyoulabinstructor.)
Wearenowgoingtousethepatternthatyoufound(andthefactthatitmadea
steadyrhythm)tofigureouthowgravityaffectsobjectsinfreefall.
Remember,uptothispointinthesemester,theonlythingweknowabout
gravityisthatwhenyoudropsomethingitfalls.Butwhatdoesitdowhenit
falls?That’swhatwe’reheretofigureout
1. Yourpatternproducedasteadyrhythm.Justtorecap,thatmeansthatthe
timeintervalbetweenbeatsstayed_____________________foreachpairofbeats.
Hm…Anintervaloftimethatstaysconsistent.Meaningitdoesn’tchange,as
thethingfalls.Hm.Thatremindsmeofsomething…somethingfromLAB1.
Thatsoundslikea…a… u n i t
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a
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!!!
2. Here’stheplan.Wewanttoknowhowaboutthemotionofobjectsduring
freefall.Inparticular,wewanttoknowwhethertheirspeedischanging,
andifit’schanging,howit’schanging.Well,instantaneousspeedmightbe
tricky,butweknowhowtocalculateaveragespeed.Writedownthe
definitionofaveragespeed.
3. Calculatethedistancetraveledbytheboltsbetweeneachpairofbeats.
(You’vealreadyfiguredthisout;yes,it’sthatsimple.)
4. Calculatetheaveragespeedoftheboltsbetweeneachpairofbeats.(Ifyou
hadnboltsonyourstring,youshouldendupwithn-1averagespeeds.)Your
answersshouldbeincm/beat(orm/beat).Noticethatwedon’tknowhow
manyseconds=1beat.Noticethatthisdoesnotmatter.
5. Calculatethechangeinaveragespeedfrombeattobeat.Inotherwords,
calculatethechangeinaveragespeedovertime.
Whatunitsshouldthisbein?
Hint:Thinkabouttheunitsyouusedforaveragespeed.Thenthinkaboutthe
factthatthisischangeinaveragespeedovertime.
6. Whatconclusioncanyoudrawaboutthemotionofobjectsinfreefall?Does
theirspeedstaythesameastheyfallordoesitchange(accelerate)?Iftheir
speedchanges,doestheiraccelerationchange(jerk)?Iftheiracceleration
changes,howdoesitchange?
Hint:thinkbacktoTheGreatDogRace.Inthatproblem,youusedthesame
methodofcomparingaveragespeedstoapproximateacceleration.
F. AHypotheticalScenario
Inordertobetterunderstandyourdataandyourconclusion,performthefollowing
thoughtexperiment.
1. Imaginethatyouareinanalternateuniversewithdifferentlawsofphysics.
Inthisuniverse,whenyoudroppedastringwithPatternB,itproduceda
steadyrhythm.
2. DothesameanalysisyoudidinpartE(especiallysteps3-5)forPatternB.
3. Calculatethechangeinthechangeintheaveragespeed,duringeachbeat.
Whatunitswouldthisbein?
4. Whatconclusionswouldyoudrawaboutthemotionofobjectsinfree-fallin
thisimaginaryalternateuniverse?Doestheirspeedstaythesameastheyfall
ordoesitchange(accelerate)?Iftheirspeedchanges,doestheiracceleration
change(jerk)?Iftheiraccelerationchanges,doesitgoupordown?Does
theirjerkchangetoo,oristhatconstant?