英文版大学物理功和能

Chapter7&8EnergyandConservationLaw1.WorkandPower2.KineticEnergy&Work-EnergyPrinciple3.ConservativeandNonconservativeForces4.PotentialEnergy5.ConservationofEnergy7-1WorkandPower(P147-)sTheworkdonebyaforceindisplacingabodyasthescalarproductofand.FsFs1.Work研究力和运动的空间过程关系。Workisascalar,nodirection.,,0dπ2π0d2π,0d2π0positivework;ConstantForce(includingitsdirection)zerowork;negativework.rFrFWcosExplanations:(1)Iftheforceisconstantinthewholepath,sFrrFrFWABBA)(dABFArBrsoFsdABWhenaparticlemovesfromAtoBalongacurvepath,thetotalworkdonebytheforceequalstheintegraloffromAtoB:F(2)Workdonebyavaryingforce:ABrrs—displacementfromAtoBBABASFWWddWorkisdependantonthereferenceframe.If4321FFFFF321321dddd(3)Workdonebyseveralforces:fififizzzyyyxxxBAzyxBAzFyFxFzFyFxFrFWddd)ddd(d(4)Specialexpressioninscalarproduct:and,kFjFiFFzyx.ddddzkjyxirTheworkdonebyseveralforces=algebraicsumoftheworkdonebytheindividualforce.(5)Geometricalrepresentationofwork:Fxx1x2dxTheworkdonebyaforceequalstheareaundertheFversusxcurve——变力曲线与位移轴在两点x1,x2之间所包围的面积.(6)Unitofwork:Dimensionis:MLT–2L=ML2T–2InSIsystem,1N·m=1J(joule)=1kg·m2/s2xFxFxFW=0W0W06Example)(42NjiyFCalculatetheworkbytheforcewhentheparticlemovesfromx1=2(m)tox2=3(m)inthefollowingcases:1.Thetrajectoryisaparabolayx422.Thetrajectoryisastraightline64xyXYO23125.2yx4264xyTheforceontheparticleisWorkdependsonpath.JdydxxdyydxdyFdxFAyyxxyxyxyx8.104)2/(42)(491322,,121212211XYO23125.2yx4264xybazyxBAdzFdyFdxFrdFAJdydxxdyydxdyFdxFAyyxxyxyxyx25.2142/)6(42)(49132,,221212211)(42NjiyFSolution:Interactionforcebetweenm1andm22dddAAA11m2mo1r2r12f21f2112ff1L2L212112rfrfdd221112rfrfdd)(2112rrfdd1212rfd12rdDisplacementofm1w.r.ttom212fForceonm1bym221211212rfrfAddd1221,ffWorkofapairofforcesWehaveusedthisconclusionbefore21211212rfrfAdddWorkbypairofnormalforces21AAAdddmMmrNd0WorkbypairoffrictionforcesmMrrfAdmMrrfd0Totalworkisnegative.MmmNrfmMrdCommonexampleDoyouknowthatitistheresultofworkbypairofforces?2.Power(功率)(P186)cosddddFvvFtrFtWPInstantaneouspower:TheinstantaneouspowerPisdefinedastherateatwhichworkisperformed.TheSIunitofpoweristhewatt,1W=1J/s1horsepower=1hp=746WsFWdcosd,ddcosandtvmmaFttvsddvmvtvtvmsFdddddcosabavbvsdFAparticlemovesfromatobalonganarbitrarypath.andmayvaryfrompointtopointalongthepath.dsFababvvKKmvmvvvmWba222121dThatis,KKKWifnet7-2Work-KineticEnergyTheorem(P156-)BecauseWegetWecanalsowritedAasAs222pppmmmvv=vddddddAFrmrmtvvvd()dd2dvvvvvvvv211ddd()d()22Ammmvvvvv2dd2pAmAnotherapproach:dddcosddddddDeduceddddcosWeshouldgetusedtothiskindofderivation.Networkdoneonanobjectequalstothechangeinitskineticenergy.Explanations:(1)Workisthemeasurementsforthechangeinthekineticenergy(K)ofabody.ifif,0,0KKWKKWIf——Bodygainsthekineticenergy.—Bodyloses“K”&doesworkoutside.(2)Bothworkand“K”arescalars.Theyhavesameunitsanddimensions;“K”onlydependsonthespeedofinitialandfinalstates,butworkdependsontherealprocess(动能是状态量,功是过程量).(4)BothWandKdependonRF.Work-kineticenergytheoremisonlyholdforinertialRF.LookatexamplesinSec.7-4afterclass.(3)Forasystemwithmoreparticles,work-kineticenergytheoremshouldbe:Thesumworkdoneonasystembyallexternalandinternalforcesequaltothechangeinkineticenergyofthesystem(质点系动能定理系统外力和内力做功总和等于系统动能的增量).KintextnetExample:Asimplependulumofmassm=1kgisreleasedfrompositiono=30o.ItmovesinacirculararcofradiusR=1minaverticalplane.Usethework-kineticenergytheoremtodeterminethespeedofthependulumbobattheangle=10o.Solution:G:constant:variableFToROdsdGFTsFsGsFWTdddnetsFTdsGWdnet)cos(cos0mgRKKKWifnet2f0g21)cos(cosmvmgRWm/s53.1)cos(cos20gRvGsmgsgmW)(netCBsGsGWddnet0RABB′C〞C′OCG''CmgBFT7-3ConservativeandNonconservativeForces1.WorkdonebyanditsfeaturesgFrFWddjyixrjmgFddd,mghymgymgWfigxyomgyiyfabcdherdConsideringabodyundermgnearthesurfaceofEarth,fromatobalongthepathofacb.Theworkdonebythegravity:(P168)fid)dd()(d)(yyymgyjximgjrmgjWThefeatureofthegravity:Wgonaparticledependsonlyontheinitialandfinalposition(orheight),anddoesnotdependontherealpathtakenbytheparticle.1.0mghmghWaebcabcaaebaebca,)(fimghyymgWaebmghyymgWbca)(fiWgonaparticlemovingaroundaclosedpath=0.2.xyomgyiyfabcdheikxFsBasedonHooke’slaw:2.Workdonebyanditsfeatures(P172)sF2f2is2121kxkxWhavethesamefeatures!gsFandFOxiABxfxsF3.Conservative&nonconservativeforces2i2f2121ddfikxkxxkxxFWxxMathematically,thetwocommonfeaturesofcanbewrittenas:gsFandFThenetworkdonebyconservativeforce(保守力)onaparticlemovingaroundanyclosedpathiszero.LrFW0dDefinition1:BAsFconstantdDefinition2:Workdonebyaconservativeforceisrecoverableorindependenceofpath