合力所做的功等于分力所做功的代数和.ppt

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,Work: varying forces or along a curve,合力所做的功等于分力所做功的代数和。,Example: Find the work done by F when particle m is slowly lifted to the present position.,Solution 1:,Solution 2:,（1）平面直角坐标系(planar orthogonal coordinate system),Work in different coordinate systems,（2）平面“自然”坐标系 (planar intrinsic system),（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 work: independent of the path of the body; depends only on the starting and ending points 引力的功： 与路径无关，仅仅取决于起始和终点的位置,Case study 2: Work done by elastic forces,0,Work done by elastic forces: 弹力的功 independent of the path of the body; depends only on the starting and ending points,Rule of signs: 正负号,W0, 弹力做功 “Work” can be stored and recovered. “功”可以储存和释放,Conservative and nonconservative forces: 保守力和非保守力 Work done by a conservative force 保守力的功： (1) Reversible, “work” can be stored in a “BANK”; 可逆，功可以被储存 (2) Independent of the path of the body; 与路径无关 (3) Zero work for closed path.闭合路径做功为零,The water is said to possess kinetic energy since it is moving. It gets this energy because it is falling through a gravitational field.,Potential energy(势能) Energy associated with the position of a system. Stored in a system, later recovered. 与相互作用物体的位置有关的能量。 Work by conservative forces potential energy,势能的增量等于保守力所做功的负值.,Gravitational potential energy,Elastic potential energy,(2)势能 保守力,梯度：,Example: find gravity from gravitational potential V=mgy,Solution:,(3) 1D Energy diagram 一维势能曲线,平衡条件,Stable equilibrium 稳定平衡？ Unstable equilibrium不稳定平衡？,Stable equilibrium 稳定平衡条件：,保守力 的判据：,保守力的判据：,Summary on potential energy Work done by a conservative force can be represented in terms of a potential energy Potential energy is a shared property of the system, not one particle. (3) Components of force are In vector form,Kinetic energy (动能) Energy associated with the motion is T=1/2mv2 A moving object has the ability to do work A scalar quantity,T=1/2mv2,Work-energy theorem: The work done by the net force on a particle equals the change in the particles kinetic energy 动能定理: 运动质点的动能的增加等于其它物体对它所做的功.,Kinetic energy T=1/2mv2 is also the ability to do work 运动质点速度改变而所作出的功,牛顿第三定律:,运动质点的1/2mv2 值的减少正等于它所做的功.,Conservation of mechanical energy 机械能守恒原理,Work-energy theorem: The total work done by the net force on a particle equals the change in the particles kinetic energy Potential energy:, Mechanical energy is conserved when only conservative forces do work.,Mechanical energy: When only gravitation does work: (1) Near the earths surface 质点高度变化不大: (2) High above the earths surface 质点高度变化很大: When only elastic force does work: 弹性力场:, 机械能守恒原理适合于由若干个物体组成的系统（如果系统内只有保守力作功）,Work-energy theorem: 功能原理,作用于质点的力F All forces,Fc所作的功Wc可用势能的减少来表示.,Fd所作的功Wn不（可）用势能的减少来表示. Dissipative 耗散,The work done by all external and nonconservative forces equals the change in mechanical energy 系统机械能的增量等于外力的功和非保守力内力的功的总和。,The Law of Conservation of Energy 能量守恒定律,Energy is never created or destroyed; it only changes form. 在封闭系统内，不论发生何种变化过程，各种形式的能量可以互相转化，但能量的总和是恒量。,功总是与能量变化或交换的过程相联系着的，而能量代表着系统在一定状态时所具有的特征，能量的量值只决定于系统的状态，系统在一定的状态时，就具有一定的能量。 能量是系统状态的单值函数。,Momentum Theorem 动量、动量定理 Momentum (动量):,Impulse (冲量 I):,（惯性定律的另一表达式）,（分量的守恒关系）,Conservation of Momentum 动量守恒,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 . 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 a