题目内容
如图所示,半径为R的四分之一圆弧支架,支架底ab离地面距离4R,圆弧边缘C处有一个小定滑轮,一轻绳两端分别系着质量为m1 m2的物体(可视为质点),挂在定滑轮两边,且m1大于m2,开始时两物体均静止。(不计一切摩擦)
求:(1)m1经过最低点a时的加速度。
(2)若m1经过最低点时绳断开,m1落地点离a的水平距离为多少?
(3)为使 m1能到达a点m1与m2之间必须满足什么关系?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152083923491.gif)
求:(1)m1经过最低点a时的加速度。
(2)若m1经过最低点时绳断开,m1落地点离a的水平距离为多少?
(3)为使 m1能到达a点m1与m2之间必须满足什么关系?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152083923491.gif)
(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208423933.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152084232563.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208438462.gif)
(1)如图将m1的运动分解,
,m1 m2组成的系统机械能守恒,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152084701041.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208485958.gif)
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208423933.gif)
(2)绳断后m1做平抛运动,平抛时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152085161449.gif)
(3)由
可知当
时
可到达a点。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208454491.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152084701041.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208485958.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208423933.gif)
(2)绳断后m1做平抛运动,平抛时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152085161449.gif)
(3)由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208423933.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208438462.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115208548219.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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