《大學物理簡明教程》 課件 4-1 Momentum

m1m2Inthegym,therockclimber(ofmassm1)isprotectedbyanotherperson(ofmassm2).Dowerequirethepersononthegroundtobeheavier?Ifnot,theoneonthegroundshouldnotbetoolight.Canyoufindtheminimumrequirementforthemassesandotherparameters?T=m1gm2gθNfs

(a)

(thespeedofsound,orspeedofabullet)Theactualspeedismuchlowerthanthat,soitmustbelimitedbythefactof“terminalspeed”.

Thespeedofraindropisveryclosetothe“terminalspeed”,9.78m/s.

raindropspeedvsdiameterRhinoceros：Runningat40km/hDragonfly：flyingat40km/hDoyoufeelthesame,whentheyaremovingtowardsyou?Dragonfly：3gramsPistolbullet：3gramsRhino：3000kgMomentumandtheConservationofMomentum67

TherateofchangeofmomentumDifferentiatebothsideswithrespecttotime,Newton’ssecondlaw?

Impulse:changeinmomentumImpulse:

DifferentialformIntegralform

(1)Impulseisavector,alsoaprocessquantity.Discussion:(2)Theaverageforceoveratimeinterval

theimpulse

linearmomentumtheoremprocessquantityvs

instantaneousquantityExample:Kickingafootball11Howlargeistheimpulse?Whichdirection?IfthecontacttimeΔt=0.01

s,howstrongistheaverageforceofkicking?CenterofMassxyzOInternalforce：Objectswithinthesystemexertonotherobjectsinthesystem.Externalforce：Forcesonobjectsofthesystemareexertedbyobjectsoutsidethesystem.InternalforceandexternalforceNewton’sthirdlaw!14Forasystemofparticles,thetotalmomentumchanges…

HasnothingtodowithinternalforcesWhenthenetexternalforceonasystemiszero,thetotalmomentumremainsconstant----thelawofconservationofmomentum15Iftheastronauthasainitialtotalmassof150kg,thenejects100ggasataspeedof1000m/s,whatisthespeedhewillgain?v=0.67m/sProblem-SolvingStrategy:ConservationofMomentum16Problem-SolvingStrategy:ConservationofMomentum17m=60kgM=2000kgvman=5m/svelephant=?Initiallythemanandtheelephantareatrest

Momentumconservation

Manandelephant19v0v=0vfvfTwoblocksconnectedbyaropeInitially,BlockCisatrest,BlockBismovingtotherightatthevelocityofv0,andtheropebetweenthemisloose.Aftertheropebecomestense,BlockBandCaremovingatthesamevelocity.Whatisthisvelocityvf

?NofrictionIsthemomentumconserved?Whataretheinitialandfinalmomenta?mCmByes

20ropebecomingtense=effectivecollisionDuringcollision

externalforcescanbeneglected!totalmomentumisconservedWhataboutifanexternalforceisalsoverystrong,comparablewiththatlargeinternalforce?Initialv0=0Three-blocksproblemv0=0v0=0hvfvfvfNofrictionmCmBmAInitially,allthreeblocksareatrest.TheropebetweenBlockBandCisloose.TheropebetweenBlockAandBistense.BlockAstarttomovedownduetotheweight.Initially,allthreeblocksareatrest.TheropebetweenBlockBandCisloose.AtthemomenttheropebetweenBlockBandCbecomestense,allblocksaremovingatthesamespeed.Whatisthisspeedvf

?Isthemomentumconservedbef