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IntroductoryPhysics

PHYS101

Dr RichardH.CyburtOfficeHoursAssistantProfessorofPhysics

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PHYS101

PHYS101:IntroductoryPhysicsLecture:8:00-9:15am,TRScienceBuilding400Lab1:3:00-4:50pm,FScienceBuilding304

Lab2:1:30-3:20pm,MScienceBuilding304



PHYS101

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PHYS101

IntroductoryPhysics

PHYS101

PHYS101

DouglasAdamsHitchhiker’sGuidetotheGalaxy

You’realreadyknowphysics!Youjustdon’tnecessarilyknowtheterminologyandlanguageweuse!!!

PhysicsofNASCARPhysicsofAngerBirds

PHYS101

Inclass!!

PHYS101

Thislecturewillhelpyouunderstand:ImpulseMomentum&theImpulse-MomentumTheoremSolvingImpulse&MomentumProblems

PHYS101

Section9.1Impulse

©2015PearsonEducation,Inc.

ImpulseAcollision isashort-durationinteractionbetweentwoobjects.

Duringacollision,ittakestimetocompresstheobject,andittakestimefortheobjecttore-expand.

Thedurationofacollisiondependsonthematerials.


ImpulseWhenkickingasoccerball,theamountbywhichtheballiscompressedisameasureofthemagnitudeoftheforcethefootexertsontheball.

Theforceisappliedonlywhiletheballisincontactwiththefoot.

Theimpulseforce isalargeforceexertedduringashortintervaloftime.


ImpulseTheeffectofanimpulsiveforceisproportionaltotheareaundertheforce-versus-timecurve.

Theareaiscalledtheimpulse Joftheforce.


QuickCheck9.6

Two1.0kgstationarycueballsarestruckbycuesticks.Thecuesexerttheforcesshown.Whichballhasthegreaterfinalspeed?

◦ Ball1◦ Ball2◦ Bothballshavethesamefinalspeed.


10 N

QuickCheck9.6

Two1.0kgstationarycueballsarestruckbycuesticks.Thecuesexerttheforcesshown.Whichballhasthegreaterfinalspeed?

◦ Ball1◦ Ball2◦ Bothballshavethesamefinalspeed.


ImpulseItisusefultothinkofthecollisionintermsofanaverage forceFavg.

Favg isdefinedastheconstantforcethathasthesamedurationΔt andthesameareaundertheforcecurveastherealforce.


Impulse

ImpulsehasunitsofN× s,butN× sareequivalenttokg×m/s.

Thelatterarethepreferredunitsforimpulse.

Theimpulseisavector quantity,pointinginthedirectionoftheaverageforcevector:


Example9.1FindingtheimpulseonabouncingballArubberballexperiencestheforceshowninFIGURE9.4asitbouncesoffthefloor.

a. Whatistheimpulseontheball?

b. Whatistheaverageforceontheball?


Example9.1Findingtheimpulseonabouncingball(cont.)PREPARE Theimpulseistheareaundertheforcecurve.Heretheshapeofthegraphistriangular,sowe’llneedtousethefactthattheareaofatriangleis ´ height´ base.


Example9.1Findingtheimpulseonabouncingball(cont.)SOLVE a.Theimpulseis

b. FromEquation9.1,J =Favg ∆t,wecanfindtheaverageforcethatwouldgivethissameimpulse:


Example9.1Findingtheimpulseonabouncingball(cont.)ASSESS Inthisparticularexample,theaveragevalueoftheforceishalfthemaximumvalue.Thisisnotsurprisingforatriangularforcebecausetheareaofatriangleishalf thebasetimestheheight.


Section9.2Momentum&theImpulse-MomentumTheorem


MomentumandtheImpulse-MomentumTheoremIntuitivelyweknowthatgivingakicktoaheavyobjectwillchangeitsvelocitymuchlessthangivingthesamekicktoalightobject.

Wecancalculatehowthefinalvelocityisrelatedtotheinitialvelocity.


FromNewton’ssecondlaw,theaverageaccelerationofanobjectduringthetimetheforceisbeingappliedis

Theaverageaccelerationisrelatedtothechangeinthevelocityby

Wecombinethosetwoequationstofind

MomentumandtheImpulse-MomentumTheorem


MomentumandtheImpulse-MomentumTheoremWecanrearrangethatequationintermsofimpulse:

Momentum istheproductoftheobject’smassandvelocity.Ithasunitsofkg×m/s.


MomentumandtheImpulse-MomentumTheoremMomentumisavector quantitythatpointsinthesamedirectionasthevelocityvector:

Themagnitude ofanobject’smomentumissimplytheproductoftheobject’smassandspeed.


MomentumandtheImpulse-MomentumTheorem


TheImpulse-MomentumTheoremImpulseandmomentumarerelatedas:

Theimpulse-momentumtheorem statesthatanimpulsedeliveredtoanobjectcausestheobject’smomentumtochange.

Impulsecanbewrittenintermsofitsx- andy-components:


TheImpulse-MomentumTheorem


QuickCheck9.2

A2.0kgobjectmovingtotherightwithspeed0.50m/sexperiencestheforceshown.Whataretheobject’sspeedanddirectionaftertheforceends?

◦ 0.50m/sleft◦ Atrest◦ 0.50m/sright◦ 1.0m/sright◦ 2.0m/sright


QuickCheck9.2

A2.0kgobjectmovingtotherightwithspeed0.50m/sexperiencestheforceshown.Whataretheobject’sspeedanddirectionaftertheforceends?

◦ 0.50m/sleft◦ Atrest◦ 0.50m/sright◦ 1.0m/sright◦ 2.0m/sright


Dpx = Jx or pfx = pix + Jx

QuickCheck9.4

Aforcepushesthecartfor1s,startingfromrest.Toachievethesamespeedwithaforcehalfasbig,theforcewouldneedtopushfor

◦ s◦ s◦ 1s◦ 2s◦ 4s


1412

QuickCheck 9.4

Aforcepushesthecartfor1s,startingfromrest.Toachievethesamespeedwithaforcehalfasbig,theforcewouldneedtopushfor

A. sB. sC. 1sD. 2sE. 4s

1412


Example9.2CalculatingthechangeinmomentumAballofmassm =0.25kgrollingtotherightat1.3m/sstrikesawallandreboundstotheleftat1.1m/s.

Whatisthechangeintheball’smomentum?

Whatistheimpulsedeliveredtoitbythewall?


Example9.2Calculatingthechangeinmomentum(cont.)PREPARE AvisualoverviewoftheballbouncingisshowninFIGURE9.8.Thisisanewkindofvisualoverview,oneinwhichweshowthesituation“before”and“after”theinteraction.We’llhavemoretosayaboutbefore-and-afterpicturesinthenextsection.Theballismovingalongthex-axis,sowe’llwritethemomentumincomponentform,asinEquation9.7.Thechangeinmomentumisthenthedifferencebetweenthefinalandinitialvaluesofthemomentum.Bytheimpulse-momentumtheorem,theimpulseisequaltothischangeinmomentum.


[InsertFigure9.8(repeated)]

Example9.2Calculatingthechangeinmomentum(cont.)SOLVE The x-componentoftheinitialmomentumis

They-componentofthemomentumiszerobothbeforeandafterthebounce.Aftertheballrebounds,thex-componentis



Example9.2Calculatingthechangeinmomentum(cont.)Itisparticularlyimportanttonoticethatthex-componentofthemomentum,likethatofthevelocity,isnegative.Thisindicatesthattheballismovingtotheleft.Thechangeinmomentumis



Bytheimpulse-momentumtheorem,theimpulsedeliveredtotheballbythewallisequaltothischange,so

ASSESS Theimpulseisnegative,indicatingthattheforcecausingtheimpulseispointingtotheleft,whichmakessense.

Example9.2Calculatingthechangeinmomentum(cont.)


TheImpulse-MomentumTheoremTheimpulse-momentumtheoremtellsus

Theaverageforceneededtostopanobjectisinverselyproportional tothedurationofthecollision.

Ifthedurationofthecollisioncanbeincreased,theforceoftheimpactwillbedecreased.



Thespinesofahedgehogobviouslyhelpprotectitfrompredators.Buttheyserveanotherfunctionaswell.Ifahedgehogfallsfromatree—anotuncommonoccurrence—itsimplyrollsitselfintoaballbeforeitlands.Itsthickspinesthencushiontheblowbyincreasingthetimeittakesfortheanimaltocometorest.Indeed,hedgehogshavebeenobservedtofalloutoftreesonpurposetogettotheground!


ExampleProblemA0.5kghockeypuckslidestotherightat10m/s.Itishitwithahockeystickthatexertstheforceshown.Whatisitsapproximatefinalspeed?


QuickCheck9.5

Alightplasticcartandaheavysteelcartarebothpushedwiththesameforcefor1.0s,startingfromrest.Aftertheforceisremoved,themomentumofthelightplasticcartis________thatoftheheavysteelcart.

◦ Greaterthan◦ Equalto◦ Lessthan◦ Can’tsay.Itdependsonhowbigtheforceis.


QuickCheck 9.5

Alightplasticcartandaheavysteelcartarebothpushedwiththesameforcefor1.0s,startingfromrest.Aftertheforceisremoved,themomentumofthelightplasticcartis________thatoftheheavysteelcart.

◦ Greaterthan◦ Equalto◦ Lessthan◦ Can’tsay.Itdependsonhowbigtheforceis.


Same force, same time Þ same impulseSame impulse Þ same change of momentum

TryItYourself:WaterBalloonCatchIfyou’veevertriedtocatchawaterballoon,youmayhavelearnedthehardwaynottocatchitwithyourarmsrigidlyextended.

Thebriefcollisiontimeimpliesalarge,balloon-burstingforce.

Abetterwaytocatchawaterballoonistopullyourarmsintowardyourbodyasyoucatchit,lengtheningthecollisiontimeandhencereducingtheforceontheballoon.




Text:p.259

TotalMomentumIfthereisa system ofparticlesmoving,thenthesystemasawholehasanoverallmomentum.

The totalmomentum ofasystemofparticlesisthevectorsumofthemomentaoftheindividualparticles:


Section9.3SolvingImpulseandMomentumProblems


SolvingImpulseandMomentumProblems


Text:p.260

Example9.3ForceinhittingabaseballA150gbaseballisthrownwithaspeedof20m/s.

Itishitstraightbacktowardthepitcherataspeedof40m/s.

TheimpulsiveforceofthebatontheballhastheshapeshowninFIGURE9.10.

Whatisthemaximum forceFmax thatthebatexertsontheball?

Whatistheaverage forcethatthebatexertsontheball?


Example9.3Forceinhittingabaseball(cont.)

PREPARE Wecanmodeltheinteractionasacollision.

FIGURE9.11isabefore-and-aftervisualoverview

inwhichthestepsfromTacticsBox9.1areexplicitlynoted.

BecauseFx ispositive(aforcetotheright),weknowtheballwasinitiallymovingtowardtheleftandishitbacktowardtheright.

Thusweconvertedthestatementsaboutspeeds intoinformationaboutvelocities,with(vx)i negative.


Example9.3Forceinhittingabaseball(cont.)SOLVE Inthelastseveralchapterswe’vestartedthemathematicalsolutionwithNewton’ssecondlaw.Nowwewanttousetheimpulse-momentumtheorem:

Weknowthevelocitiesbeforeandafterthecollision,sowecanfindthechangeintheball’smomentum:


Example9.3Forceinhittingabaseball(cont.)TheforcecurveisatrianglewithheightFmax andwidth0.60ms.AsinExample9.1,theareaunderthecurveis

Accordingtotheimpulse-momentumtheorem,∆px =Jx,sowehave


Thusthemaximum forceis

UsingEquation9.1,wefindthattheaverage force,whichdependsonthecollisionduration∆t = 6.0´ 10–4 s,hasthesmallervalue:

ASSESS Fmax isalargeforce,butquitetypicaloftheimpulsiveforcesduringcollisions.

Example9.3Forceinhittingabaseball(cont.)


TheImpulseApproximationTheimpulseapproximation statesthatwecanignorethesmallforcesthatactduring thebrieftimeoftheimpulsiveforce.

Weconsideronlythemomenta andvelocitiesimmediatelybeforeandimmediatelyafterthecollisions.


QuickCheck9.1

Thecart’schangeofmomentumDpx is

◦ –20kgm/s◦ –10kgm/s◦ 0kgm/s◦ 10kgm/s◦ 30kgm/s


QuickCheck9.1

Thecart’schangeofmomentumDpx is

◦ –20kgm/s◦ –10kgm/s◦ 0kgm/s◦ 10kgm/s◦ 30kgm/s


Dpx = 10 kg m/s - (-20 kg m/s) = 30 kg m/s

Negative initial momentum because motion is to the left and vx < 0.

ExampleProblemA500kgrocketslediscoastingat20m/s.

Itthenturnsonitsrocketenginesfor5.0s,withathrustof1000N.

Whatisitsfinalspeed?


ExampleProblemAcartravelingat20m/scrashesintoabridgeabutment.

Estimatetheforceonthedriver(m=60kg)ifthedriverisstoppedby

A. A20-m-longrowofwater-filledbarrels.

B. Thecrumplezoneofhercar(~1m).Assumeaconstantacceleration.


Introductory Physics - Home | · bouncing ball A rubber ball ... The change in momentum is then...

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