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1、9IMPULSEANDMOMENTUMConceptualQuestions9.1.Thevelocitiesandmassesvaryfromobjecttoobject,sothereisnochoicebuttocomputepx=mvxforeachoneandthencompare:p1x==(20g)(1m/s)20gm/sp2x==(20g)(2m/s)40gm/sp3x==(10g)(2m/s)20gm/sp4x==(10g)(1m/s)10gm/sp5x=.(200g)(01m/s)=20gm/sSotheanswerisp21
2、354x>==>ppppxxxx.9.2.Impulsegivesameasureoftheeffectofaforceactingoveraperiodoftime.Duringthetimeanetforceactsonanobject,theobjectwillaccelerateanditsvelocitywillchange.Impulsegivesameasureoftheeffectofaforcewithoutspecifyingthedetailedtimedependenceoftheforce.9.3.Anisolateds
3、ystemisacollectionofinteractingobjectsforwhichalloutsideforces(i.e.,forcesfromobjectsoutsidethesystem)arebalanced;thatis,inanisolatedsystem,allexternalforcescanceleachotherout.9.4.Whenthequestiontalksaboutforces,times,andmomenta,weimmediatelythinkoftheimpulse-momentumtheorem,
4、whichtellsusthat,tochangethemomentumofanobject,wemustexertanetexternalforceonitoveraddtimeinterval:Δ=pFtavgΔ.Becauseequalforcesareexertedoverequaltimes,theimpulsesareequalandthechangesinmomentumareequal.Becausebothcartsstartfromrest,thechangeinmomentumofeachisthesameasthefina
5、lmomentumofeach,sotheirfinalmomentaareequal.Noticethat,toanswerthequestion,wedonotneedtoknowthemassofeithercart,oreventhespecifictimeinterval(aslongasitisthesameforbothcarts).9.5.Theimpulse-momentumtheorytellsusthatthechangeinmomentumofanobjectisrelatedtothenetforceonddtheobj
6、ectandthelengthoftimetheforcewasapplied.Mathematically,Δ=pFtavgΔ.Thesameforceappliedtothetwocartsresultsinalargeraccelerationforthelessmassiveplasticcart(Newton’ssecondlaw),enablingittotravelthe1-mdistanceinashortertime.Therefore,theplasticcarthasasmallerchangeinmomentumthant
7、heleadcart.Becausethefinalmomentumofeachcartisequaltotheirchangeinmomentum(zeroinitialmomentum),thefinalmomentumoftheplasticcartislessthanthatoftheleadcart.9.6.Inthisstory,Carlosiscorrect.Duringtheshorttimeofthebullet-blockcollisionotherforcesarenegligiblecomparedtotheforcebe
8、tweenthebulletandblock,sointheimpulseapproximationmomentumisconserve
