题目内容
如图所示,abc是光滑的轨道,其中ab是水平的,bc为与ab相切的位于竖直平面内的半圆,半径R=0.30m。质量m=0.20kg的小球A静止在轨道上,另一质量M=0.60kg、速度V0=5.5m/s的小球B与小球A正碰。已知相碰后小球A经过半圆的最高点c落到轨道上距b点为,
处,重力加速度
,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010533892135.jpg)
(1)碰撞结束后,小球A和B的速度的大小。
(2)试论证小球B是否能沿着半圆轨道到达c点。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053296591.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053358664.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010533892135.jpg)
(1)碰撞结束后,小球A和B的速度的大小。
(2)试论证小球B是否能沿着半圆轨道到达c点。
(1)6m/s 3.5m/s (2)不能
试题分析:(1)以v1表示小球A碰后的速度,以v2表示小球B碰后的速度,v1/表示小球A在圆周最高点的速度,则小球脱离轨道后做平抛运动,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053405168.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053420691.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053436676.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053452984.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053483772.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053514951.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010535301282.png)
(2)假设B球能到达C点,则满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053654803.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010536701091.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001053686948.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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