题目内容
(14分)
长为L的轻绳一端系一小球,另一端悬于O点。小球从与竖直方向成
角处释放,到最低点与一钉子C相碰后绕C做圆周运动,若半径
,欲使小球刚好能通过最高点,则
(1)
角应为多大?
(2)若小球释放位置不变,则到达最低点时碰钉子后瞬间绳子对小球的拉力等于多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241245339014935.jpg)
长为L的轻绳一端系一小球,另一端悬于O点。小球从与竖直方向成
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533870219.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533885329.gif)
(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533870219.gif)
(2)若小球释放位置不变,则到达最低点时碰钉子后瞬间绳子对小球的拉力等于多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241245339014935.jpg)
(14分)解:(1)(7分)从A→D过程中,
在D处,由于小球刚好能通过最高点,则有
其中![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533948304.gif)
解以上方程得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533963274.gif)
2)(7分)从A→B,由机械能守恒有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124534072516.gif)
在B处受力如图,由牛顿第二定律
其中![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533948304.gif)
解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124534104289.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533916592.gif)
在D处,由于小球刚好能通过最高点,则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533932367.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533948304.gif)
解以上方程得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533963274.gif)
2)(7分)从A→B,由机械能守恒有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124534072516.gif)
在B处受力如图,由牛顿第二定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124534072394.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124533948304.gif)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124534104289.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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