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Dr RichardH.CyburtOfficeHoursAssistantProfessorofPhysics
Myoffice:402cintheScienceBuilding
Myphone:(304)384-6006
Myemail:[email protected]
Inpersonoremailisthebestwaytogetaholdofme.
TRF9:30-11:00amF12:30-2:00pm
Meetingsmayalsobearrangedatothertimes,byappointment
Checkmyscheduleonmyofficedoor.
PHYS101
PHYS101:IntroductoryPhysicsLecture:8:00-9:15am,TRScienceBuilding400Lab1:3:00-4:50pm,FScienceBuilding304
Lab2:1:30-3:20pm,MScienceBuilding304
Lab3:3:30-5:20pm,MScienceBuilding304
Lab20:6:00-7:50pm,MScienceBuilding304
PHYS101
MasteringPhysicsOnlineGotoHYPERLINK"http://www.masteringphysics.com."www.masteringphysics.com.◦ UnderRegisterNow,selectStudent.◦ Confirmyouhavetheinformationneeded,thenselectOK!Registernow.
◦ Enteryourinstructor’sCourseID(RCYBURTPHYS101),andchooseContinue.
◦ EnteryourexistingPearsonaccountusername andpassword andselectSignin.◦ YouhaveanaccountifyouhaveeverusedaPearsonMyLab &Masteringproduct,suchasMyMathLab,MyITLab,MySpanishLab,or
MasteringChemistry.
◦ Ifyoudon’thaveanaccount,select Create andcompletetherequiredfields.◦ Selectanaccessoption.◦ Entertheaccesscodethatcamewithyourtextbookorwaspurchasedseparatelyfromthebookstore.
PHYS101
Midterm2Therewillbeabonusassignment,basedonyourexam◦ Willearnyouextrapointsonyourexam◦ Itwillbeonlineasahomework◦ Youmustdobetteronthisassignment,thanyourtesttogetbonuspoints◦ Bonus=30%x(Homework– Midterm)
BonusHomeworkisOnline,dueOct17,12:59pm (justbeforelabsstartfortheday)
AfterBonusHWisdue,therewillbeasignoutsheetinmyoffice◦ Youmustsigntogetyourexam
PHYS101
You’realreadyknowphysics!Youjustdon’tnecessarilyknowtheterminologyandlanguageweuse!!!
PhysicsofNASCARPhysicsofAngerBirds
PHYS101
Thislecturewillhelpyouunderstand:ImpulseMomentum&theImpulse-MomentumTheoremSolvingImpulse&MomentumProblems
PHYS101
ImpulseAcollision isashort-durationinteractionbetweentwoobjects.
Duringacollision,ittakestimetocompresstheobject,andittakestimefortheobjecttore-expand.
Thedurationofacollisiondependsonthematerials.
©2015PearsonEducation,Inc.
ImpulseWhenkickingasoccerball,theamountbywhichtheballiscompressedisameasureofthemagnitudeoftheforcethefootexertsontheball.
Theforceisappliedonlywhiletheballisincontactwiththefoot.
Theimpulseforce isalargeforceexertedduringashortintervaloftime.
©2015PearsonEducation,Inc.
ImpulseTheeffectofanimpulsiveforceisproportionaltotheareaundertheforce-versus-timecurve.
Theareaiscalledtheimpulse Joftheforce.
©2015PearsonEducation,Inc.
QuickCheck9.6
Two1.0kgstationarycueballsarestruckbycuesticks.Thecuesexerttheforcesshown.Whichballhasthegreaterfinalspeed?
◦ Ball1◦ Ball2◦ Bothballshavethesamefinalspeed.
©2015PearsonEducation,Inc.
10 N
QuickCheck9.6
Two1.0kgstationarycueballsarestruckbycuesticks.Thecuesexerttheforcesshown.Whichballhasthegreaterfinalspeed?
◦ Ball1◦ Ball2◦ Bothballshavethesamefinalspeed.
©2015PearsonEducation,Inc.
ImpulseItisusefultothinkofthecollisionintermsofanaverage forceFavg.
Favg isdefinedastheconstantforcethathasthesamedurationΔt andthesameareaundertheforcecurveastherealforce.
©2015PearsonEducation,Inc.
Impulse
ImpulsehasunitsofN× s,butN× sareequivalenttokg×m/s.
Thelatterarethepreferredunitsforimpulse.
Theimpulseisavector quantity,pointinginthedirectionoftheaverageforcevector:
©2015PearsonEducation,Inc.
Example9.1FindingtheimpulseonabouncingballArubberballexperiencestheforceshowninFIGURE9.4asitbouncesoffthefloor.
a. Whatistheimpulseontheball?
b. Whatistheaverageforceontheball?
©2015PearsonEducation,Inc.
Example9.1Findingtheimpulseonabouncingball(cont.)PREPARE Theimpulseistheareaundertheforcecurve.Heretheshapeofthegraphistriangular,sowe’llneedtousethefactthattheareaofatriangleis ´ height´ base.
©2015PearsonEducation,Inc.
Example9.1Findingtheimpulseonabouncingball(cont.)SOLVE a.Theimpulseis
b. FromEquation9.1,J =Favg ∆t,wecanfindtheaverageforcethatwouldgivethissameimpulse:
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Example9.1Findingtheimpulseonabouncingball(cont.)ASSESS Inthisparticularexample,theaveragevalueoftheforceishalfthemaximumvalue.Thisisnotsurprisingforatriangularforcebecausetheareaofatriangleishalf thebasetimestheheight.
©2015PearsonEducation,Inc.
MomentumandtheImpulse-MomentumTheoremIntuitivelyweknowthatgivingakicktoaheavyobjectwillchangeitsvelocitymuchlessthangivingthesamekicktoalightobject.
Wecancalculatehowthefinalvelocityisrelatedtotheinitialvelocity.
©2015PearsonEducation,Inc.
FromNewton’ssecondlaw,theaverageaccelerationofanobjectduringthetimetheforceisbeingappliedis
Theaverageaccelerationisrelatedtothechangeinthevelocityby
Wecombinethosetwoequationstofind
MomentumandtheImpulse-MomentumTheorem
©2015PearsonEducation,Inc.
MomentumandtheImpulse-MomentumTheoremWecanrearrangethatequationintermsofimpulse:
Momentum istheproductoftheobject’smassandvelocity.Ithasunitsofkg×m/s.
©2015PearsonEducation,Inc.
MomentumandtheImpulse-MomentumTheoremMomentumisavector quantitythatpointsinthesamedirectionasthevelocityvector:
Themagnitude ofanobject’smomentumissimplytheproductoftheobject’smassandspeed.
©2015PearsonEducation,Inc.
TheImpulse-MomentumTheoremImpulseandmomentumarerelatedas:
Theimpulse-momentumtheorem statesthatanimpulsedeliveredtoanobjectcausestheobject’smomentumtochange.
Impulsecanbewrittenintermsofitsx- andy-components:
©2015PearsonEducation,Inc.
QuickCheck9.2
A2.0kgobjectmovingtotherightwithspeed0.50m/sexperiencestheforceshown.Whataretheobject’sspeedanddirectionaftertheforceends?
◦ 0.50m/sleft◦ Atrest◦ 0.50m/sright◦ 1.0m/sright◦ 2.0m/sright
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QuickCheck9.2
A2.0kgobjectmovingtotherightwithspeed0.50m/sexperiencestheforceshown.Whataretheobject’sspeedanddirectionaftertheforceends?
◦ 0.50m/sleft◦ Atrest◦ 0.50m/sright◦ 1.0m/sright◦ 2.0m/sright
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Dpx = Jx or pfx = pix + Jx
QuickCheck9.4
Aforcepushesthecartfor1s,startingfromrest.Toachievethesamespeedwithaforcehalfasbig,theforcewouldneedtopushfor
◦ s◦ s◦ 1s◦ 2s◦ 4s
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1412
QuickCheck 9.4
Aforcepushesthecartfor1s,startingfromrest.Toachievethesamespeedwithaforcehalfasbig,theforcewouldneedtopushfor
A. sB. sC. 1sD. 2sE. 4s
1412
©2015PearsonEducation,Inc.
Example9.2CalculatingthechangeinmomentumAballofmassm =0.25kgrollingtotherightat1.3m/sstrikesawallandreboundstotheleftat1.1m/s.
Whatisthechangeintheball’smomentum?
Whatistheimpulsedeliveredtoitbythewall?
©2015PearsonEducation,Inc.
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.
©2015PearsonEducation,Inc.
[InsertFigure9.8(repeated)]
Example9.2Calculatingthechangeinmomentum(cont.)SOLVE The x-componentoftheinitialmomentumis
They-componentofthemomentumiszerobothbeforeandafterthebounce.Aftertheballrebounds,thex-componentis
©2015PearsonEducation,Inc.
[InsertFigure9.8(repeated)]
Example9.2Calculatingthechangeinmomentum(cont.)Itisparticularlyimportanttonoticethatthex-componentofthemomentum,likethatofthevelocity,isnegative.Thisindicatesthattheballismovingtotheleft.Thechangeinmomentumis
©2015PearsonEducation,Inc.
[InsertFigure9.8(repeated)]
Bytheimpulse-momentumtheorem,theimpulsedeliveredtotheballbythewallisequaltothischange,so
ASSESS Theimpulseisnegative,indicatingthattheforcecausingtheimpulseispointingtotheleft,whichmakessense.
Example9.2Calculatingthechangeinmomentum(cont.)
©2015PearsonEducation,Inc.
TheImpulse-MomentumTheoremTheimpulse-momentumtheoremtellsus
Theaverageforceneededtostopanobjectisinverselyproportional tothedurationofthecollision.
Ifthedurationofthecollisioncanbeincreased,theforceoftheimpactwillbedecreased.
©2015PearsonEducation,Inc.
TheImpulse-MomentumTheorem
Thespinesofahedgehogobviouslyhelpprotectitfrompredators.Buttheyserveanotherfunctionaswell.Ifahedgehogfallsfromatree—anotuncommonoccurrence—itsimplyrollsitselfintoaballbeforeitlands.Itsthickspinesthencushiontheblowbyincreasingthetimeittakesfortheanimaltocometorest.Indeed,hedgehogshavebeenobservedtofalloutoftreesonpurposetogettotheground!
©2015PearsonEducation,Inc.
ExampleProblemA0.5kghockeypuckslidestotherightat10m/s.Itishitwithahockeystickthatexertstheforceshown.Whatisitsapproximatefinalspeed?
©2015PearsonEducation,Inc.
QuickCheck9.5
Alightplasticcartandaheavysteelcartarebothpushedwiththesameforcefor1.0s,startingfromrest.Aftertheforceisremoved,themomentumofthelightplasticcartis________thatoftheheavysteelcart.
◦ Greaterthan◦ Equalto◦ Lessthan◦ Can’tsay.Itdependsonhowbigtheforceis.
©2015PearsonEducation,Inc.
QuickCheck 9.5
Alightplasticcartandaheavysteelcartarebothpushedwiththesameforcefor1.0s,startingfromrest.Aftertheforceisremoved,themomentumofthelightplasticcartis________thatoftheheavysteelcart.
◦ Greaterthan◦ Equalto◦ Lessthan◦ Can’tsay.Itdependsonhowbigtheforceis.
©2015PearsonEducation,Inc.
Same force, same time Þ same impulseSame impulse Þ same change of momentum
TryItYourself:WaterBalloonCatchIfyou’veevertriedtocatchawaterballoon,youmayhavelearnedthehardwaynottocatchitwithyourarmsrigidlyextended.
Thebriefcollisiontimeimpliesalarge,balloon-burstingforce.
Abetterwaytocatchawaterballoonistopullyourarmsintowardyourbodyasyoucatchit,lengtheningthecollisiontimeandhencereducingtheforceontheballoon.
©2015PearsonEducation,Inc.
TotalMomentumIfthereisa system ofparticlesmoving,thenthesystemasawholehasanoverallmomentum.
The totalmomentum ofasystemofparticlesisthevectorsumofthemomentaoftheindividualparticles:
©2015PearsonEducation,Inc.
Example9.3ForceinhittingabaseballA150gbaseballisthrownwithaspeedof20m/s.
Itishitstraightbacktowardthepitcherataspeedof40m/s.
TheimpulsiveforceofthebatontheballhastheshapeshowninFIGURE9.10.
Whatisthemaximum forceFmax thatthebatexertsontheball?
Whatistheaverage forcethatthebatexertsontheball?
©2015PearsonEducation,Inc.
Example9.3Forceinhittingabaseball(cont.)
PREPARE Wecanmodeltheinteractionasacollision.
FIGURE9.11isabefore-and-aftervisualoverview
inwhichthestepsfromTacticsBox9.1areexplicitlynoted.
BecauseFx ispositive(aforcetotheright),weknowtheballwasinitiallymovingtowardtheleftandishitbacktowardtheright.
Thusweconvertedthestatementsaboutspeeds intoinformationaboutvelocities,with(vx)i negative.
©2015PearsonEducation,Inc.
Example9.3Forceinhittingabaseball(cont.)SOLVE Inthelastseveralchapterswe’vestartedthemathematicalsolutionwithNewton’ssecondlaw.Nowwewanttousetheimpulse-momentumtheorem:
Weknowthevelocitiesbeforeandafterthecollision,sowecanfindthechangeintheball’smomentum:
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Example9.3Forceinhittingabaseball(cont.)TheforcecurveisatrianglewithheightFmax andwidth0.60ms.AsinExample9.1,theareaunderthecurveis
Accordingtotheimpulse-momentumtheorem,∆px =Jx,sowehave
©2015PearsonEducation,Inc.
Thusthemaximum forceis
UsingEquation9.1,wefindthattheaverage force,whichdependsonthecollisionduration∆t = 6.0´ 10–4 s,hasthesmallervalue:
ASSESS Fmax isalargeforce,butquitetypicaloftheimpulsiveforcesduringcollisions.
Example9.3Forceinhittingabaseball(cont.)
©2015PearsonEducation,Inc.
TheImpulseApproximationTheimpulseapproximation statesthatwecanignorethesmallforcesthatactduring thebrieftimeoftheimpulsiveforce.
Weconsideronlythemomenta andvelocitiesimmediatelybeforeandimmediatelyafterthecollisions.
©2015PearsonEducation,Inc.
QuickCheck9.1
Thecart’schangeofmomentumDpx is
◦ –20kgm/s◦ –10kgm/s◦ 0kgm/s◦ 10kgm/s◦ 30kgm/s
©2015PearsonEducation,Inc.
QuickCheck9.1
Thecart’schangeofmomentumDpx is
◦ –20kgm/s◦ –10kgm/s◦ 0kgm/s◦ 10kgm/s◦ 30kgm/s
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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?
©2015PearsonEducation,Inc.