题目内容
如图4-1所示:摆球的质量为m,从偏离水平方向30°的位置由静释放,设绳子为理想轻绳,求小球运动到最低点A时绳子受到的拉力是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137475822327.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137475822327.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113747613697.gif)
设悬线长为l,下球被释放后,先做自由落体运动,直到下落高度为h=2lsin
,处于松驰状态的细绳被拉直为止。这时,小球的速度竖直向下,大小为
。
当绳被拉直时,在绳的冲力作用下,速度v的法向分量
减为零(由于绳为理想绳子,能在瞬间产生的极大拉力使球的法向速度减小为零,相应的动能转化为绳的内能);小球以切向分量
开始作变速圆周运动到最低点,在绳子拉直后的过程中机械能守恒,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137477381130.gif)
在最低点A,根据牛顿第二定律,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113747754557.gif)
所以,绳的拉力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113747629200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113747645428.gif)
当绳被拉直时,在绳的冲力作用下,速度v的法向分量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113747691204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113747707488.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137477381130.gif)
在最低点A,根据牛顿第二定律,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113747754557.gif)
所以,绳的拉力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113747613697.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目