大学物理双语版奥本汉姆课件Chap9-Moment.ppt

Chapter9MomentumandtheConservationofMomentum LinearImpulseandMomentumImpulse MomentumTheoremandConservationofMomentumN IILawfortheMotionoftheCenterofMassSystemsofVariableMass 9 1LinearImpulse MomentumTheorem theimpulse 冲量 offorce 1 Impulse momentumtheorem 研究力和运动的时间积累过程关系 Netlinearimpulsedeliveredtoaparticleequalsthechangeinlinearmomentumoftheparticle 物体在运动过程中所受合外力的冲量 等于该物体动量的增量 Descriptions 1 Fshouldbethesumofallexternalforces Whentheforceisconstant thedirectionofJisassameastheforce ifFisvariable thedirectionofJisdeterminedbytheintegralof 2 Bothandarevectors Theyhavesameunitsanddimensions ThistheoremisonlyholdforIRF 3 Inreality oneoftenuseitscomponentform 4 ThemagnitudeoftheimpulseisequaltotheareaundertheF t curve LookatProblem28ofP227 Apitched140gbaseball inhorizontalflightwithaspeedof39m s isstruckbyabatandtheballleavesthebatwithaspeedof45m s atanupwardangle上偏of30o a whatimpulseactontheball b Iftheimpacttimeis1 2ms whataverageforceactonthebaseball b Example Momentumtheoremofparticlesystem ThereareNparticlesinasystem Theequationofmotionforparticleiis forthewholesystemis 9 2ConservationofMomentum P202 note impulse momentumtheoremofparticlesystem Theimpulseofexternalforcesactingonasystem thechangeofmomentumoftheentiresystem Ifnonetexternalforceactsonaparticles system totallinearmomentumofthesystemcannotchange Noexceptionstothislawhavebeendiscovered SoitisconsideredtobemorefundamentalthanNewton ssecondlawinbothmacroscopicandmicroscopicphysicalworlds 1 Conditionsofvalidity Netforcescanbeneglectedinthecaseofcollision strike explosion andsoon 2 Conclusion Onlyexternalforcecanchangethestateofmotionofasystem 3 Ifcomponentofnetexternalforceonasystemalonganaxisiszero thecomponentofmomentumofthesystemalongthataxisdoesnotchange 4 Itisonlysuitableforinertialreferenceframe Solution AgunmountedonwheelsofmassMshootsaprojectileofmassmwithmuzzle 出口 velocityofv 对炮车 atanangle abovethehorizontal Findthehorizontalrecoil 反冲 speedVofthegun 求 炮车反冲速度V neglectfriction Therecoilspeed Example Answer AflatcarofweightWcanrollwithoutfrictionalongahorizontalstraighttrack Initially amanofweightwisstandingonthecar whichismovingtotheleftwithspeedvo Whatisthechangeinvelocityofthecarifthemanrunstorightsothathisspeedrelativetothecarisvrel Thedirectionofitisassameastheoneofvrel Example ThecenterofmassofN particlesystemisapointthatmovesasthoughallofmasswereconcentra tedthereandallexternalforceswereappliedthere Definethepositionofthecenterofmass CM ofN particlesystemtobe Similarrelationstotheyandzcomponents 9 3TheCenterofMass 质心运动定理 Ifaparticlesystemexertedbyzeroforce thevelocityofmasscenterkeepconstant N IILawforthemotionofthecenterofmass Thesumofallforcesactingonasystem totalmassofthesystemtimesofitscenterofmass Thecenterofmassofallpartsofthebodiesmoveslikeasingleparticleactedbythesamenetexternalforce gravity Asfigureshown aboatL 4m M 150kg Itisinitiallyrestonthewater Whenamen m 50kg walksfromtheheadtothetailoftheboat whatarethedistancesofthemenandboatrelativetothebeach respectively 人和船对岸各移动的距离 neglectthefrictionfromwater Initial Final constant 质心初始静止 Example Letanddenotethevelocityofboatandmenrelativetothebeachatanyinstant then 9 4SystemsofVariableMass RocketPropulsion AsFig 9 33shown asystemhaschangedinmassfromMtoM dMintimedt wehave Withalittlealgebraandnote Thenadynamicequationforthissystemshouldbe Lookatexamplesin 9 10afterclass Where thetwotermsonitsrightsiderepresentsthesumofexternalforceonthemassMandtheforceexertedonitduetotheadditionofmass Forarocketpropulsion Thethrust 推力 oftherocketengine Itdependsonthede