788 Work and Energy 2 Work energy principle(动能定理p157-158)) A particle moves from a to b along an arbitrary path. F and ds may vary from point to point along the path. 当外力移动物体从q到b过程中,力对物体作功,将外 力分解为切向分力和法向分力 卩=∫FdF=∫FF-∫FdB f b d t =m- 0△F dt d ds mudu=-m0 dt
7&8 Work and Energy A particle moves from a to b along an arbitrary path. and may vary from point to point along the path. ds F 2 Work Energy Principle (动能定理p157-158)） 当外力移动物体从a到b过程中，力对物体作功，将外 力分解为切向分力和法向分力 a F b Fn F W F dr F dr F ds = t = t = t F m d d t v = 2 1 2 2 2 1 2 1 d d d d 2 1 2 1 v v v v v v v v v s m m m t W = m = = −
788 Work and Energ ◆动能(状态函数) E 2m W=E-E ◆动能定理 Work-energy principle 合外力对质点所作的功等于质点动能的增量 Net work done on an object equals to the change in its kinetic energy. P157
7&8 Work and Energy 动能（状态函数） m p E m 2 2 1 2 2 k = v = W = Ek2 −Ek1 动能定理 Work-energy principle 合外力对质点所作的功,等于质点动能的增量 . Net work done on an object equals to the change in its kinetic energy. P157
788 Work and Energy This principle is not a new independent law Rather. it has been derived from the definitions of work and kinetic energy using Newtons second law. p158
7&8 Work and Energy This principle is not a new independent law. Rather, it has been derived from the definitions of work and kinetic energy using Newton’s second law. p158
788 Work and Energy Descriptions (1) Work is the measurements for the change in the kinetic energy(“K”) of a body fw>0,K>ki--Body gains the kinetic energy. W<0,K<K;- Body loses“K”& does work outside (2) Both work and“K” are scalars. They have same units and dimensions; "K"only depends on the speed of initial and final states, but work depends on the real proce动能是状态量,功是过程量) Example 7-10
7&8 Work and Energy Descriptions: (1) Work is the measurementsfor the change in the kinetic energy (“K”) of a body. f i f i W K K If W K K 0, 0, ——Body gains the kinetic energy. —Body loses “K” & does work outside. (2) Both work and “K” are scalars. They have same units and dimensions; “K” only depends on the speed of initial and final states, but work depends on the real process(动能是状态量,功是过程量). Example 7-10
788 Work and Energy 3 Work Energy Principle for a system with more particles 如果研究的对象为质点系,动 U10=> 能定理又如何表示?以最简单 的两个质点组成的质点系为研 f12 究对象。 两个质点质量为 21 m1、m2,受外力F1、 O2△r2 F2,内力为f12、f21,初 )a2 速度为U10、U20,末速度 U)o→>U 为U1、U2,位移r,△rn
7&8 Work and Energy 3 Work Energy Principle for a system with more particles 如果研究的对象为质点系，动 能定理又如何表示？以最简单 的两个质点组成的质点系为研 究对象。 两个质点质量为 m1、 m2 ，受外力F1、 F2，内力为f12、f21，初 速度为v10、v20,末速度 为v1、v2 ,位移 为 . 1 2 r ,r 1 ' 1 2 ' 2 21 f 12 f F1 F2 r1 r2 m1 m2 v10 → v1 v20 → v2