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1、第二章牛顿运动定律2-1 牛顿运动定律力一、牛顿运动定律1、第一定律0F时，恒量V（2-1）说明：反映物体的惯性，故叫做惯性定律。给出了力的概念，指出了力是改变物体运动状态的原因。2、第二定律amF（2-2）说明：F为合力amF为瞬时关系矢量关系只适应于质点解题时常写成zzyyxxmaFmaFmaFamF（直角坐标系）（2-3）（切向）（法向）dtdvmmaFrvmmaFamFttnn2（自然坐标系）（2-4）3、第三定律11FF（2-5）说明：1F、2F在同一直线上，但作用在不同物体上。1F、2F同有同无互不抵消。二、几种常见的力1、力力是指物体间的相互作用。2、力学中常见的力（1）万有引力
2、2210rmmGF（2-6）即任何二质点都要相互吸引，引力的大小和两个质点的质量1m、2m的乘积成正比，和它们距离r的平方成反比；引力的方向在它们连线方向上。说明：通常所说的重力就是地面附近物体受地球的引力。（2）弹性力弹簧被拉伸或压缩时，其内部就产生反抗力，并企图恢复原来的形状，这种力称为弹簧的恢复力。（3）摩擦力当一物体在另一物体表面上滑动或有滑动的趋势时，在接触面上有一种阻碍它们相对滑动的力，这种力称为摩擦力。3、两种质量由惯引称为惯性质量，确定的质量称为引力质量，确定的质量mmmafmmrGmMf2/可证明：constmm惯引，适选单位可有惯引mm。以后不区别二者，统称为质量。2-2
3、力学单位制和量纲（自学）2-3 惯性系力学相对性原理一、惯性参照系在运动学中，参照系可任选，在应用牛顿定律时，参照系不能任选，因为牛顿运动定律不是对所有的参照系都适用。如图2-1，假设火车车厢的桌面是水平光滑的，在桌面上放一小球，显然小球受合外力=0，当火车以加速度a向前开时，车上人看见小球以加速度a向后运动。而对地面上人来说，小球的加速度为零。如果取地参系，小球的合外力等于零，故此时牛顿运动定律（第一、二定律）成立。如果取车厢为参照系，小球的加速度0，而作用小球的合外力0，故此时牛顿运动定律（第一、第二定律）不am图 2-1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2
4、X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5
5、V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码
6、:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R
7、5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1
8、E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4
9、A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6
10、D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1成立。凡是牛顿运动定律成立的参照系，称为惯性系。牛顿定律不成立的参照系称为非惯性系。说明：（1）一个参照系是否为惯性系，要由观察和实验来判断。天文学方面的观察证明，以太阳中心为原点，坐标轴的方向指向恒星的坐标轴是惯性系。理论证明，凡是对
11、惯性系做匀速直线运动的参照系都是惯性系。（2）地球是否为惯性系？因为它有自转和公转，所以地球对太阳这个惯性系不是作匀速直线运动的，严格讲地球不是惯性系。但是，地球自转和公转的角速度都很小，故可以近似看成是惯性系。二、力学相对性原理在 1-3 中已讲过，参照系 E与 M，设 E是一惯性系，M相对 E以MEv做匀速直线运动，即 OM 也是一惯性系，二参照系相应坐标轴平行，在E、M上牛顿第二定律均成立，设一质点 P1质量为 m，相对 E、M有）相对）相对MamFEamFPMMPEE(（2-7）设 P相对 E、M的速度分别为PEv、PMv，有MEPMPEvvv（2-8）上式两边对t求一阶导数有PMPE
12、aa（2-9）可见，P 对 E 和 M的加速度相同。综上可知，对于不同的惯性系，牛顿第二定律有相同的形式（见（2-7），在一惯性系内部所做的任何力学实验，都不能确定该惯性系相对其它惯性系是否在运动（见（2-9），这个原理称为力学相对性原理或伽利略相对性原理。2-4 牛顿定律应用举例例 2-1:如图 2-2，水平地面上有一质量为M的物体，静止于地面上。物体与地面间的静摩擦系数为s，若要拉动物体，问最小的拉力是多少？沿何方向？解：研究对象：M 受力分析：M受四个力，重力 P，拉力T，地面的正压力N，地面对它的摩擦力f，见受力图 2-3。牛顿第二定律：合力：aMfNTPfNTPFFM图 2-2FM图
13、 2-3NPfxyo文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2
14、F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档
15、编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO1
16、0R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10
17、X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 H
18、R4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5
19、M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1分量式：取直角坐标系x 分量：MafF cosy 分量：0sinPNF物体启动时，有0cosfF物体刚启动时，摩擦力为最大静摩擦力，即Nfs，由解出
20、 N，求得f为：)sin(FPfs代中：有)sin/(cosssMgF可见：)(FF。minTT时，要求分母)sin(coss最大。设cossin)(sA0sincossddAstg0cossin22sdAdstg时，maxAAminFF。sarctg代入中，得：222211111/ssssssMgMgFF方向与水平方向夹角为sarctg时，即为所求结果。强调：注意受力分析，力学方程的矢量式、标量式（取坐标）。例 2-2：质量为m的物体被竖直上抛，初速度为0v，物体受到的空气阻力数值为KVf，K 为常数。求物体升高到最高点时所用时间及上升的最大高度。解：研究对象：m 受力分析：m受两个力，重力
21、 P及空气阻力f，如图 2-4。牛顿第二定律：合力：fPFamfPy 分量：dtdVmKVmgdtKVmgmdVxyofp抛出点 y=0图 2-4文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E
22、7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A
23、7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D
24、6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X
25、5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V
26、1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:
27、CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1即dtmKVmgdV1
28、tvvdtmKVmgdV010dtmKVmgKVmgK1ln10)(0KVmgeKVmgtmKmgKeKVmgKVtmK1)(100V时，物体达到了最高点，可有0t为)1ln(ln000mgKVKmmgKVmgKmtdtdyVVdtdydtmgKeKVmgKVdtdyttmKty00001)(1mgtKeKVmgKmytmK11)(02mgtKeKVmgKmtmK11)(020tt时，maxyy，)1ln(11)(0)1ln(02max0mgKVKmmgKeKVmgKmymgKVKmmK)1ln(11)(022002mgKVgKmmgKVmgKVmgKm)1ln()(0220002mgKVgK
29、mKVmgKVKVmgKm)1ln(0220mgKVgKmKmV例 2-3：如图 2-5，长为 l 的轻绳，一端系质量为m的小球，另一端系于原点o，开始时小球处于最低位置，若小球获得如图所示的初速度0v，小球将在竖直面内作圆周运动，求:小球在任意位置的速率及绳的张力。解：研究对象：m 文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6
30、ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A
31、2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文
32、档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO
33、10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A1
34、0X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7
35、HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T
36、5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1受力分析：小球受两个力，即重力gm，拉力nF，如图 2-6。牛顿定律：amgmFn应用自然坐标系，运动到处时，分量方程有，ne方向：lvmmamgFnn2cosie方向：dtdvmmamgtsin由有：ddvlvddvdtdddvdtdvgsin即dsi nlgvdv作如下积分：00dsi nlgvdvvv有)l g(c o s)vv(121202得：)l g(c o svv1220v代中，得：)2cos3(20gglvmFn例 2-4：如图 2-6，一根轻绳穿过定滑轮，轻绳两
37、端各系一质量为1m和2m的物体，且21mm，设滑轮的质量不计，滑轮与绳及轴间摩擦不计，定滑轮以加速度0a相对地面向上运动，试求两物体相对定滑轮的加速度大小及绳中张力。解：研究对象：1m、2m受力分析：1m、2m各受两个力，即重力及绳拉力，如图 2-7。牛顿定律设1m对定滑轮及地加速度为1a、1a，2m对定滑轮及地加速度为2a、2a，1m：)(0111111aamamTgm2m：)(0222222aamamTgm如图所选坐标，并注意aaa21，TTT21，有)()(022011aamTgmaamTgm解得：)(02121agmmmmateneonFgmovvA图 2-51a2a1m2m0a图 2
38、-6gm1图 2-7gm21T2Txy文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D
39、6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X
40、5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V
41、1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:
42、CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5
43、A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E
44、7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1)(202121agmmmmT例 2-5：如图 2-8，质量为 M 的三角形劈置于水平光滑桌面上，另一质量为m的木块放在 M 的斜
45、面上，m与 M 间无摩擦。试求 M 对地的加速度和m对 M 的加速度。解：研究对象：m、M受力分析：M 受三个力，重力gM，正压力N，地面支持力 N。m受两个力，重力gm，M 的支持力N，如图 2-9 所取坐标系，设 M 对地加速度为Ma，m对 M 的加速度为mMa，m对地的加速度为ma，有MmMmaaa由牛顿得二定律有：m：)(MmMaamNgmx 分量：)cos(sinMmMaamNy 分量：sincosmMmaNmgM：NNMaNMsin由、有：22sinsin)(sincossinmMcgMmamMmgaMmM强调：相对运动公式的应用。Mm图 2-8NgMNMayxmMagmN图 2-
46、9文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:
47、CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5
48、A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E
49、7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A
50、7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D6 ZK2X5A2F5V1文档编码:CO10R5A10X1E7 HR4A7T5M6D