合力所做的功等于分力所做功的代数和

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1、Chapter4WorkandEnergyWork:Everydaymeaning:anyactivitythatrequiresmuscularormentaleffort.Inphysics:theworkdoneonanobjectbyaforceinavectordisplacementistheirinnerproduct(scalar)—thesamemagnitudeofforce:positive,mines,zeroworkFrWork:varyingforcesoralon

2、gacurve合力所做的功等于分力所做功的代数和。TmgFExample:FindtheworkdonebyFwhenparticlemisslowlyliftedtothepresentposition.Solution1:Solution2:TmgF（1）平面直角坐标系(planarorthogonalcoordinatesystem)xyOxr0r1yFrs0s1FsWorkindifferentcoordinatesystems（2）平面“自然”坐标系(planarintrins

3、icsystem)r1rOr0F(,)（3）极坐标系(planarpolarsystem)Power(功率)Everydaymeaning:energyorforceInphysics:thetimerateatwhichworkisdone力的功率等于力与受力点速度的标积Summaryonwork功的性质(1)Generallyspeaking,workisdependentonthepath.功是过程量，一般与路径有关。(2)Workisascalarwithmagnitudea

4、ndsigns.功是标量，但有正负。(3)Workdonebyresultantofallforcesequals合力的功为各分力的功的代数和。Casestudy1:Workdonebygravitation引力的功两个质点之间在万有引力作用下相对运动时，以M所在处为原点,M指向m的方向为矢径r的正方向。m受的引力方向与矢径方向相反。m在M的万有引力的作用下从a点运动到b点，万有引力的功:Gravitationalwork:independentofthepathofthebody;depend

5、sonlyonthestartingandendingpoints引力的功：与路径无关，仅仅取决于起始和终点的位置Casestudy2:WorkdonebyelasticforceskOabkOacbOakkOabkOa<0Workdonebyelasticforces:弹力的功independentofthepathofthebody;dependsonlyonthestartingandendingpointsRuleofsigns:正负号W<0,外力做功，W>0,弹力做功“Work”can

6、bestoredandrecovered.“功”可以储存和释放Conservativeandnonconservativeforces:保守力和非保守力Workdonebyaconservativeforce保守力的功：(1)Reversible,“work”canbestoredina“BANK”;可逆，功可以被储存(2)Independentofthepathofthebody;与路径无关(3)Zeroworkforclosedpath.闭合路径做功为零ABL1L2等价Energyisdef

7、inedastheabilitytodowork.Workisdefinedasthetransferofenergy.Thewaterissaidtopossesskineticenergysinceitismoving.Itgetsthisenergybecauseitisfallingthroughagravitationalfield.Potentialenergy(势能)Energyassociatedwiththepositionofasystem.Storedinasystem,

8、laterrecovered.与相互作用物体的位置有关的能量。Workbyconservativeforcespotentialenergy势能的增量等于保守力所做功的负值.(1)保守力做功势能GravitationalpotentialenergyElasticpotentialenergy(2)势能保守力梯度：Example:findgravityfromgravitationalpotentialV=mgySolution:(3)1DEnergydiagram一维势能曲线xU(x)