Download PHYS101

IntroductoryPhysics
PHYS101
Dr RichardH.CyburtOfficeHours
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PHYS101
PHYS101:IntroductoryPhysics
400
Lecture:8:00-9:15am,TRScienceBuilding
Lab1:3:00-4:50pm,FScienceBuilding304
Lab2:1:30-3:20pm,MScienceBuilding304
Lab3:3:30-5:20pm,MScienceBuilding304
Lab20:6:00-7:50pm,MScienceBuilding304
PHYS101
MasteringPhysicsOnline
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PHYS101
Midterm2
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PHYS101
IntroductoryPhysics
PHYS101
DouglasAdams
Hitchhiker’sGuidetotheGalaxy
PHYS101
You’realreadyknowphysics!
Youjustdon’tnecessarilyknowtheterminologyand
languageweuse!!!
PhysicsofNASCAR
PhysicsofAngerBirds
PHYS101
Inclass!!
PHYS101
Thislecturewillhelpyouunderstand:
Impulse
Momentum&theImpulse-MomentumTheorem
SolvingImpulse&MomentumProblems
PHYS101
Section9.1Impulse
©2015PearsonEducation,Inc.
Impulse
Acollision isashort-durationinteractionbetweentwoobjects.
Duringacollision,ittakestimetocompresstheobject,andittakestimeforthe
objecttore-expand.
Thedurationofacollisiondependsonthematerials.
©2015PearsonEducation,Inc.
Impulse
Whenkickingasoccer
ball,theamountbywhich
theballiscompressedisa
measureofthemagnitude
oftheforcethefootexerts
ontheball.
Theforceisappliedonly
whiletheballisincontact
withthefoot.
Theimpulseforce isalarge
forceexertedduringashort
intervaloftime.
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Impulse
Theeffectofanimpulsive
forceisproportionalto
theareaunderthe
force-versus-timecurve.
Theareaiscalledthe
impulse Joftheforce.
©2015PearsonEducation,Inc.
QuickCheck9.6
Two1.0kgstationarycueballsarestruckbycuesticks.Thecuesexerttheforces
shown.Whichballhasthegreaterfinalspeed?
10 N
◦ Ball1
◦ Ball2
◦ Bothballshavethesamefinalspeed.
©2015PearsonEducation,Inc.
QuickCheck9.6
Two1.0kgstationarycueballsarestruckbycuesticks.Thecuesexerttheforces
shown.Whichballhasthegreaterfinalspeed?
◦ Ball1
◦ Ball2
◦ Bothballshavethesamefinalspeed.
©2015PearsonEducation,Inc.
Impulse
Itisusefultothinkofthe
collisionintermsofan
average forceFavg.
Favg isdefinedastheconstant
forcethathasthesame
durationΔt andthesame
areaundertheforcecurve
astherealforce.
©2015PearsonEducation,Inc.
Impulse
ImpulsehasunitsofN× s,butN× sareequivalentto
kg× m/s.
Thelatterarethepreferredunitsforimpulse.
Theimpulseisavector quantity,pointinginthedirectionoftheaverageforce
vector:
©2015PearsonEducation,Inc.
Example9.1Findingtheimpulseona
bouncingball
Arubberballexperiencesthe
forceshowninFIGURE9.4
asitbouncesoffthefloor.
a. Whatistheimpulseonthe
ball?
b. Whatistheaverageforce
ontheball?
©2015PearsonEducation,Inc.
Example9.1Findingtheimpulseona
bouncingball(cont.)
PREPARE Theimpulseisthe
areaundertheforcecurve.
Heretheshapeofthegraph
istriangular,sowe’llneed
tousethefactthatthearea
ofatriangleis ´ height´ base.
©2015PearsonEducation,Inc.
Example9.1Findingtheimpulseona
bouncingball(cont.)
SOLVE a.Theimpulseis
b. FromEquation9.1,
J =Favg ∆t,wecanfind
theaverageforcethat
wouldgivethissameimpulse:
©2015PearsonEducation,Inc.
Example9.1Findingtheimpulseona
bouncingball(cont.)
ASSESS Inthisparticular
example,theaveragevalue
oftheforceishalfthe
maximumvalue.Thisisnot
surprisingforatriangular
forcebecausetheareaofa
triangleishalf thebase
timestheheight.
©2015PearsonEducation,Inc.
Section9.2Momentum&
theImpulse-Momentum
Theorem
©2015PearsonEducation,Inc.
MomentumandtheImpulseMomentumTheorem
Intuitivelyweknowthat
givingakicktoaheavy
objectwillchangeits
velocitymuchlessthan
givingthesamekicktoa
lightobject.
Wecancalculatehowthe
finalvelocityisrelatedto
theinitialvelocity.
©2015PearsonEducation,Inc.
MomentumandtheImpulseMomentumTheorem
FromNewton’ssecondlaw,theaverageaccelerationofanobjectduringthe
timetheforceisbeingappliedis
Theaverageaccelerationisrelatedtothechangeinthevelocityby
Wecombinethosetwoequationstofind
©2015PearsonEducation,Inc.
MomentumandtheImpulseMomentumTheorem
Wecanrearrangethatequationintermsofimpulse:
Momentum istheproductoftheobject’smassandvelocity.Ithasunitsofkg×
m/s.
©2015PearsonEducation,Inc.
MomentumandtheImpulseMomentumTheorem
Momentumisavector quantity
thatpointsinthesamedirection
asthevelocityvector:
Themagnitude ofanobject’s
momentumissimplythe
productoftheobject’smass
andspeed.
©2015PearsonEducation,Inc.
MomentumandtheImpulseMomentumTheorem
©2015PearsonEducation,Inc.
TheImpulse-MomentumTheorem
Impulseandmomentumarerelatedas:
Theimpulse-momentumtheorem statesthatanimpulsedeliveredtoan
objectcausestheobject’smomentumtochange.
Impulsecanbewrittenintermsofitsx- andy-components:
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TheImpulse-MomentumTheorem
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QuickCheck9.2
A2.0kgobjectmovingtotherightwithspeed0.50m/sexperiencestheforce
shown.Whataretheobject’sspeedanddirectionaftertheforceends?
◦
◦
◦
◦
◦
0.50m/sleft
Atrest
0.50m/sright
1.0m/sright
2.0m/sright
©2015PearsonEducation,Inc.
QuickCheck9.2
A2.0kgobjectmovingtotherightwithspeed0.50m/sexperiencestheforce
shown.Whataretheobject’sspeedanddirectionaftertheforceends?
◦
◦
◦
◦
◦
0.50m/sleft
Atrest
0.50m/sright
1.0m/sright
2.0m/sright
Dpx = Jx or pfx = pix + Jx
©2015PearsonEducation,Inc.
QuickCheck9.4
Aforcepushesthecartfor1s,startingfromrest.Toachievethesamespeed
withaforcehalfasbig,theforcewouldneedtopushfor
1
4
1
2
◦ s
◦ s
◦ 1s
◦ 2s
◦ 4s
©2015PearsonEducation,Inc.
QuickCheck 9.4
Aforcepushesthecartfor1s,startingfromrest.Toachievethesame
speedwithaforcehalfasbig,theforcewouldneedtopushfor
1
A. 4 s
B. 1 s
2
C. 1s
D. 2s
E. 4s
©2015PearsonEducation,Inc.
Example9.2Calculatingthechangein
momentum
Aballofmassm =0.25kg
rollingtotherightat1.3m/s
strikesawallandrebounds
totheleftat1.1m/s.
Whatisthechangeintheball’s
momentum?
Whatistheimpulsedeliveredtoitby
thewall?
©2015PearsonEducation,Inc.
Example9.2Calculatingthechangein
momentum(cont.) [InsertFigure9.8(repeated)]
PREPARE Avisualoverviewof
theballbouncingisshownin
FIGURE9.8.Thisisanewkind
ofvisualoverview,oneinwhich
weshowthesituation“before”
and“after”theinteraction.We’ll
havemoretosayaboutbeforeand-afterpicturesinthenext
section.Theballismovingalong
thex-axis,sowe’llwritethemomentumincomponentform,asinEquation9.7.
Thechangeinmomentumisthenthedifferencebetweenthefinalandinitial
valuesofthemomentum.Bytheimpulse-momentumtheorem,theimpulseis
equaltothischangeinmomentum.
©2015PearsonEducation,Inc.
Example9.2Calculatingthechangein
momentum(cont.) [InsertFigure9.8(repeated)]
SOLVE The x-component
oftheinitialmomentumis
They-componentofthe
momentumiszeroboth
beforeandafterthebounce.
Aftertheballrebounds,
thex-componentis
©2015PearsonEducation,Inc.
Example9.2Calculatingthechangein
momentum(cont.) [InsertFigure9.8(repeated)]
Itisparticularlyimportant
tonoticethatthex-component
ofthemomentum,likethat
ofthevelocity,isnegative.
Thisindicatesthattheball
ismovingtotheleft.The
changeinmomentumis
©2015PearsonEducation,Inc.
Example9.2Calculatingthechangein
momentum(cont.)
Bytheimpulse-momentum
theorem,theimpulse
deliveredtotheballby
thewallisequaltothis
change,so
ASSESS Theimpulseisnegative,
indicatingthattheforcecausingtheimpulseispointingtotheleft,whichmakes
sense.
©2015PearsonEducation,Inc.
TheImpulse-MomentumTheorem
Theimpulse-momentumtheoremtellsus
Theaverageforceneededtostopanobjectisinverselyproportional tothe
durationofthecollision.
Ifthedurationofthecollisioncanbeincreased,theforceoftheimpactwillbe
decreased.
©2015PearsonEducation,Inc.
TheImpulse-MomentumTheorem
Thespinesofahedgehogobviouslyhelpprotectitfrompredators.Buttheyserve
anotherfunctionaswell.Ifahedgehogfallsfromatree—anotuncommon
occurrence—itsimplyrollsitselfintoaballbeforeitlands.Itsthickspinesthen
cushiontheblowbyincreasingthetimeittakesfortheanimaltocometorest.
Indeed,hedgehogshavebeenobservedtofalloutoftreesonpurposetogettothe
ground!
©2015PearsonEducation,Inc.
ExampleProblem
A0.5kghockeypuckslidestotherightat10m/s.Itishitwithahockeystickthat
exertstheforceshown.Whatisitsapproximatefinalspeed?
©2015PearsonEducation,Inc.
QuickCheck9.5
Alightplasticcartandaheavysteelcartarebothpushedwiththesameforce
for1.0s,startingfromrest.Aftertheforceisremoved,the
momentumofthelight
plasticcartis________that
oftheheavysteelcart.
◦
◦
◦
◦
Greaterthan
Equalto
Lessthan
Can’tsay.Itdependsonhowbigtheforceis.
©2015PearsonEducation,Inc.
QuickCheck 9.5
Alightplasticcartandaheavysteelcartarebothpushedwiththesameforce
for1.0s,startingfromrest.Aftertheforceisremoved,the
momentumofthelight
plasticcartis________that
oftheheavysteelcart.
◦
◦
◦
◦
Greaterthan
Equalto
Lessthan
Can’tsay.Itdependsonhowbigtheforceis.
Same force, same time Þ same impulse
Same impulse Þ same change of momentum
©2015PearsonEducation,Inc.
TryItYourself:WaterBalloonCatch
Ifyou’veevertriedtocatchawaterballoon,youmayhavelearnedthehardway
nottocatchitwithyourarmsrigidlyextended.
Thebriefcollisiontimeimpliesalarge,balloon-burstingforce.
Abetterwaytocatchawaterballoonistopullyourarmsintowardyourbodyas
youcatchit,lengtheningthecollisiontimeandhencereducingtheforceonthe
balloon.
©2015PearsonEducation,Inc.
TheImpulse-MomentumTheorem
Text:p.259
©2015PearsonEducation,Inc.
TotalMomentum
Ifthereisa system ofparticles
moving,thenthesystemasa
wholehasanoverallmomentum.
The totalmomentum ofasystem
ofparticlesisthevectorsumof
themomentaoftheindividual
particles:
©2015PearsonEducation,Inc.
Section9.3Solving
Impulseand
MomentumProblems
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SolvingImpulseandMomentum
Problems
Text:p.260
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Example9.3Forceinhittingabaseball
A150gbaseballisthrownwitha
speedof20m/s.
Itishitstraightbacktowardthepitcherata
speedof40m/s.
Theimpulsiveforceofthebatontheballhasthe
shapeshowninFIGURE9.10.
Whatisthemaximum forceFmax thatthe
batexertsontheball?
Whatistheaverage forcethatthebatexerts
ontheball?
©2015PearsonEducation,Inc.
Example9.3Forceinhittingabaseball
(cont.)
PREPARE Wecanmodeltheinteractionasacollision.
FIGURE9.11isabefore-and-aftervisualoverview
inwhichthestepsfromTacticsBox9.1areexplicitly
noted.
BecauseFx ispositive(aforcetotheright),weknowtheballwasinitiallymoving
towardtheleftandishitbacktowardtheright.
Thusweconvertedthestatementsaboutspeeds intoinformationabout
velocities,with(vx)i negative.
©2015PearsonEducation,Inc.
Example9.3Forceinhittingabaseball
(cont.)
SOLVE Inthelastseveralchapters
we’vestartedthemathematical
solutionwithNewton’ssecond
law.Nowwewanttousethe
impulse-momentumtheorem:
Weknowthevelocitiesbefore
andafterthecollision,sowe
canfindthechangeintheball’s
momentum:
©2015PearsonEducation,Inc.
Example9.3Forceinhittingabaseball
(cont.)
Theforcecurveisatrianglewith
heightFmax andwidth0.60ms.
AsinExample9.1,thearea
underthecurveis
Accordingtothe
impulse-momentumtheorem,
∆px =Jx,sowehave
©2015PearsonEducation,Inc.
Example9.3Forceinhittingabaseball
(cont.)
Thusthemaximum forceis
UsingEquation9.1,wefindthatthe
average force,whichdependsonthe
collisionduration∆t = 6.0´ 10–4 s,
hasthesmallervalue:
ASSESS Fmax isalargeforce,butquitetypicaloftheimpulsiveforcesduringcollisions.
©2015PearsonEducation,Inc.
TheImpulseApproximation
Theimpulseapproximation statesthatwecanignorethesmallforcesthatact
during thebrieftimeoftheimpulsiveforce.
Weconsideronlythemomenta andvelocitiesimmediatelybeforeand
immediatelyafterthecollisions.
©2015PearsonEducation,Inc.
QuickCheck9.1
Thecart’schangeof
momentumDpx is
◦
◦
◦
◦
◦
–20kgm/s
–10kgm/s
0kgm/s
10kgm/s
30kgm/s
©2015PearsonEducation,Inc.
QuickCheck9.1
Thecart’schangeof
momentumDpx 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.
©2015PearsonEducation,Inc.
ExampleProblem
A500kgrocketslediscoastingat20m/s.
Itthenturnsonitsrocketenginesfor5.0s,withathrustof1000N.
Whatisitsfinalspeed?
©2015PearsonEducation,Inc.
ExampleProblem
Acartravelingat20m/scrashesintoabridgeabutment.
Estimatetheforceonthedriver(m=60kg)ifthedriverisstoppedby
A.
A20-m-longrowofwater-filledbarrels.
B.
Thecrumplezoneofhercar(~1m).Assumeaconstantacceleration.
©2015PearsonEducation,Inc.