大学物理-保守力与非保守力.ppt

1/12,一万有引力和弹性力作功的特点(Thefeaturesoftheworkdonebytheuniversalgravitational&theelasticforce),m对m的万有引力为,m移动dr时,F作元功为,1、万有引力作功(Workdonebyuniversalgravitationalforce),2/12,m从A到B的过程中F作功：,3/12,2、弹性力作功(Workdonebyelasticforce),弹性力,4/12,保守力所作的功仅决定于物体始、末位置,而与所经过的路径无关,二保守力与非保守力保守力作功的数学表达式(Theconservativeforce&Thenon-conservativeforceThemathematicalexpressionofworkbytheconservatiiveforce),Theworkdonebytheconservatiiveforceonlydependsontheinitial&finalpositionsoftheobject&isindependentofthepaththatittook.,1保守力作功的特点(Thefeatureoftheworkdonebytheconservativeforce),5/12,质点沿任意闭合路径运动一周时,保守力对它所作的功为零.,非保守力:力所作的功与路径有关(如摩擦力).,Whenanobjectmovesaroundanarbitraryclosedlooptheworkdonebyconservativeforcesonitiszero,Thenon-conservativeforce:Workdonebytheforcedependsonthepath(e.gThefrictionalforce),2保守力作功的数学表达式(Themathematicalexpressionofworkbytheconservativeforce),6/12,三势能(Potentialenergy),与相互作用的物体相对位置有关的能量.,Energydependsonoftherelativepositionoftheinteractiveobjects,引力势能Gravitionalpotentialenergy,引力的功Workofgravitionalforce,弹力的功Workofelasticforce,弹力势能Elasticpotentialenergy,7/12,物体在地球表面附近距地面高为y时,具有的引力势能称为重力势能,保守力对物体作的功等于物体势能增量的负值,保守力的功(Workofconservativeforce),重力势能(Gravitypotenial),Theworkdonebytheconservativeforceonobjectisequaltothenegativevalueoftheincrementofthepotenialenergyofthatobject,8/12,在一维情况下,作用于物体上的在Ox轴上的保守力,等于势能对坐标x的导数的负值。,TheconservativeforceactingontheobjectalongtheOxaxisisequaltothenegativederivativeofpotenialenergywithrespecttothecoordinatex,9/12,势能是状态的函数,讨论,Thepotenialenergyisafunctionofstate,势能具有相对性,势能大小与势能零点的选取有关,任意两点间的势之能差却是绝对的.,Therelativityofthepotenialenergy,thevalueofthepotenialenergydependsontheselectionofthezeropoint,thedifferenceofthepotentialenergybetweenanytwopointhasanabsolutemeaning,10/12,势能是属于物体系统的.,势能计算(Calculationofpotenialenergy),Thepotenialenergybelongtothesystemofobjects,讨论,11/12,四势能曲线(Thepotenialene