(完整word版)高一物理必修2圆周运动复习知识点总结及经典例题详细剖析(3),推荐文档.pdf

《(完整word版)高一物理必修2圆周运动复习知识点总结及经典例题详细剖析(3),推荐文档.pdf》由会员分享，可在线阅读，更多相关《(完整word版)高一物理必修2圆周运动复习知识点总结及经典例题详细剖析(3),推荐文档.pdf（15页珍藏版）》请在得力文库 - 分享文档赚钱的网站上搜索。

1、匀速圆周运动专题从现行高中知识体系来看，匀速圆周运动上承牛顿运动定律，下接万有引力，因此在高一物理中占据极其重要的地位，同时学好这一章还将为高二的带电粒子在磁场中的运动及高三复习中解决圆周运动的综合问题打下良好的基础。（一）基础知识1.匀速圆周运动的基本概念和公式（1）线速度大小，方向沿圆周的切线方向，时刻变化；（2）角速度，恒定不变量；（3）周期与频率；（4）向心力，总指向圆心，时刻变化，向心加速度，方向与向心力相同；（5）线速度与角速度的关系为，、的关系为。所以在、中若一个量确定，其余两个量也就确定了，而还和有关。2.质点做匀速圆周运动的条件（1）具有一定的速度；（2）受到的合力（向心力）

2、大小不变且方向始终与速度方向垂直。合力（向心力）与速度始终在一个确定不变的平面内且一定指向圆心。3.向心力有关说明向心力是一种效果力。任何一个力或者几个力的合力，或者某一个力的某个分力，只要其效果是使物体做圆周运动的，都可以认为是向心力。做匀速圆周运动的物体，向心力就是物体所受的合力，总是指向圆心；做变速圆周运动的物体，向心力只是物体所受合外力在沿着半径方向上的一个分力，合外力的另一个分力沿着圆周的切线，使速度大小改变，所以向心力不一定是物体所受的合外力。（二）解决圆周运动问题的步骤1.确定研究对象；2.确定圆心、半径、向心加速度方向；3.进行受力分析，将各力分解到沿半径方向和垂直于半径方向；

3、4.根据向心力公式，列牛顿第二定律方程求解。基本规律：径向合外力提供向心力（三）常见问题及处理要点1.皮带传动问题例 1：如图 1 所示，为一皮带传动装置，右轮的半径为r，a 是它边缘上的一点，左侧是一轮轴，大轮的半径为4r，小轮的半径为2r，b 点在小轮上，到小轮中心的距离为r，c 点和 d 点分别位于小轮和大轮的边缘上，若在传动过程中，皮带不打滑，则（）A.a 点与 b 点的线速度大小相等B.a 点与 b 点的角速度大小相等C.a 点与 c 点的线速度大小相等D.a 点与 d 点的向心加速度大小相等图 1 解析：皮带不打滑，故a、c 两点线速度相等，选C；c 点、b 点在同一轮轴上角速度相

4、等，半径不同，由，b 点与 c 点线速度不相等，故a 与 b 线速度不等，A 错；同样可判定a与 c 角速度不同，即a 与 b 角速度不同，B 错；设 a 点的线速度为，则 a点向文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10

5、文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:C

6、W2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5

7、W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10

8、HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R

9、7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6

10、ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M

11、4S6M10心加速度，由，所以，故，D正确。本题正确答案C、D。点评：处理皮带问题的要点为：皮带（链条）上各点以及两轮边缘上各点的线速度大小相等，同一轮上各点的角速度相同。2.水平面内的圆周运动转盘：物体在转盘上随转盘一起做匀速圆周运动，物体与转盘间分无绳和有绳两种情况。无绳时由静摩擦力提供向心力；有绳要考虑临界条件。例 1：如图 2 所示，水平转盘上放有质量为m 的物体，当物块到转轴的距离为r 时，连接物块和转轴的绳刚好被拉直（绳上张力为零）。物体和转盘间的最大静摩擦力是其正压力的倍。求：（1）当转盘的角速度时，细绳的拉力。（2）当转盘的角速度时，细绳的拉力。图 2 文档编码:CW2J8B5

12、W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10

13、HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R

14、7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6

15、ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M

16、4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10

17、文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:C

18、W2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10解析：设转动过程中物体与盘间恰好达到最大静摩擦力时转动的角速度为，则，解得（1）因为，所以物体所需向心力小于物与盘间的最大摩擦力，则物与盘产生的摩擦力还未达到最大静摩擦力，细绳的拉力仍为0，即

19、。（2）因为，所以物体所需向心力大于物与盘间的最大静摩擦力，则细绳将对物体施加拉力，由牛顿第二定律得，解得。点评：当转盘转动角速度时，物体有绳相连和无绳连接是一样的，此时物体做圆周运动的向心力是由物体与圆台间的静摩擦力提供的，求出。可见，是物体相对圆台运动的临界值，这个最大角速度与物体的质量无关，仅取决于和 r。这一结论同样适用于汽车在平路上转弯。圆锥摆：圆锥摆是运动轨迹在水平面内的一种典型的匀速圆周运动。其特点是由物体所受的重力与弹力的合力充当向心力，向心力的方向水平。也可以说是其中弹力的水平分力提供向心力（弹力的竖直分力和重力互为平衡力）。例 2：小球在半径为R 的光滑半球内做水平面内的匀

20、速圆周运动，试分析图3 中的（小球与半球球心连线跟竖直方向的夹角）与线速度v、周期 T 的关系。（小球的半径远小于R）。文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6

21、ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M

22、4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10

23、文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:C

24、W2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5

25、W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10

26、HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10图 3 解析：小球做匀速圆周运动的圆心在和小球等

27、高的水平面上（不在半球的球心），向心力 F 是重力 G 和支持力的合力，所以重力和支持力的合力方向必然水平。如图3 所示有由此可得，可见，越大（即轨迹所在平面越高），v 越大，T 越小。点评：本题的分析方法和结论同样适用于火车转弯、飞机在水平面内做匀速圆周飞行等在水平面内的匀速圆周运动的问题。共同点是由重力和弹力的合力提供向心力，向心力方向水平。3.竖直面内的圆周运动竖直面内圆周运动最高点处的受力特点及题型分类（图4）。图 4 这类问题的特点是：由于机械能守恒，物体做圆周运动的速率时刻在改变，所以物体在最高点处的速率最小，在最低点处的速率最大。物体在最低点处向心力向上，而重力向下，所以弹力必然

28、向上且大于重力；而在最高点处，向心力向下，重力也向下，所以弹力的方向就不能确定了，要分三种情况进行讨论。（1）弹力只可能向下，如绳拉球。这种情况下有，即，否则不能通过最高点；文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编

29、码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J

30、8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F

31、10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6

32、K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1

33、D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2

34、B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6

35、M10（2）弹力只可能向上，如车过桥。在这种情况下有，否则车将离开桥面，做平抛运动；（3）弹力既可能向上又可能向下，如管内转（或杆连球、环穿珠）。这种情况下，速度大小 v 可以取任意值。但可以进一步讨论：a.当时物体受到的弹力必然是向下的；当时物体受到的弹力必然是向上的；当时物体受到的弹力恰好为零。b.当弹力大小时，向心力有两解；当弹力大小时，向心力只有一解；当弹力时，向心力等于零，这也是物体恰能过最高点的临界条件。结合牛顿定律的题型例 3：如图 5 所示，杆长为，球的质量为，杆连球在竖直平面内绕轴O 自由转动，已知在最高点处，杆对球的弹力大小为，求这时小球的瞬时速度大小。图 5 解析：小球所

36、需向心力向下，本题中，所以弹力的方向可能向上也可能向下。（1）若 F向上，则，；（2）若 F向下，则，文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6

37、M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编

38、码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J

39、8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F

40、10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6

41、K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1

42、D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10点评：本题是杆连球绕轴自由转动，根据机械能守恒，还能求出小球在最低

43、点的即时速度。需要注重的是：若题目中说明小球在杆的带动下在竖直面内做匀速圆周运动，则运动过程中小球的机械能不再守恒，这两类题一定要分清。结合能量的题型例 4：一内壁光滑的环形细圆管，位于竖直平面内，环的半径为R（比细管的半径大得多），在圆管中有两个直径与细管内径相同的小球A、B，质量分别为、，沿环形管顺时针运动，经过最低点的速度都是，当 A 球运动到最低点时，B 球恰好到最高点，若要此时作用于细管的合力为零，那么、R 和应满足的关系是。解析：由题意分别对A、B 小球和圆环进行受力分析如图6 所示。对于 A 球有对于 B 球有根据机械能守恒定律由环的平衡条件而，由以上各式解得文档编码:CW2J8

44、B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F1

45、0 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K

46、4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D

47、6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B

48、9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M

49、10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码

50、:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10文档编码:CW2J8B5W2F10 HV6K4R7Y1D6 ZY2B9M4S6M10图 6 点评：圆周运动与能量问题常联系在一起，在解这类问题时，除要对物体受力分析，运用圆周运动知识外，还要正确运用能量关系（动能定理、机械能守恒定律）。连接问题的题型例 5：如图 7 所示