合力所做的功等于分力所做功的代数和初步.pptVIP

A small ball with mass m is suspended between 2 identical springs inside a box with mass M. The elastic constant of the spring is κ . The box falls freely from h (relative to the table surface) and performs a totally inelastic collision with the surface of the table. At the moment when the box starts to fall, the springs do not deform and the ball remains stationary. What is the minimum value of h such that after the totally inelastic collision between the box and the table surface, the box jumps up again? Homework: 10.4， 10.8， 10.9， 10.12 , 10.13，10.14 Momentum Theorem 动量、动量定理 Momentum (动量): Forces applied over time periods create impulses. Impulse (冲量 I): 力对时间的积分 The impulse equals the change in momentum. （惯性定律的另一表达式） （分量的守恒关系） Conservation of Momentum 动量守恒 * Chapter 4 Work and Energy Work: Everyday meaning: any activity that requires muscular or mental effort. In physics: the work done on an object by a force in a vector displacement is their inner product (scalar) —the same magnitude of force: positive, mines, zero work F ?r Work: varying forces or along a curve 合力所做的功等于分力所做功的代数和。 T mg F Example: Find the work done by F when particle m is slowly lifted to the present position. Solution 1: Solution 2: T mg F （1）平面直角坐标系(planar orthogonal coordinate system) x y O ?x r0 r1 ?y F ?r s0 s1 F ?s Work in different coordinate systems （2）平面“自然”坐标系 (planar intrinsic system) r1 ?r ? O r0 F ? ? (?,?) （3）极坐标系 (planar polar system) Power (功率) Everyday meaning: energy or force In physics: the time rate at which work is done 力的功率等于力与受力点速度的标积 Summary on work 功的性质 (1) Generally speaking, work is dependent on the path. 功是过程量，一般与路径有关。 (2) Work is a scalar with magnitude and signs. 功是标量，但有正负。 ?(3) Work done by resultant of all forces equals 合力的功为各分力的功的代数和。 Case study 1: Work done by gravitation 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:??????????????? ????? Gravitational w