题目内容
如图所示,在圆柱形屋顶中心天花板O点,挂一根L="3" m的细绳,绳的下端挂一个质量
为
的小球,已知绳能承受的最大拉力为10 N。小球在水平面内做圆周运动,当速度逐渐增大到绳断裂后,小球以
的速度落在墙边。求这个圆柱形房屋的高度
和半径
。(g取10 m/s2)?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241138435551066.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843461303.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843477301.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843493407.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843508206.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843524204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241138435551066.gif)
4.8m
设绳与竖直方向夹角为θ,则
,所以
,
小球在绳断时离地高度为:
小球做匀速圆周运动的半径为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843633687.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843649953.gif)
联立①②③④式求得:
,平抛运动时间为:
,水平距离为:
,
圆柱半径为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843555597.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843571289.gif)
小球在绳断时离地高度为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843586491.gif)
小球做匀速圆周运动的半径为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843617436.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843633687.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843649953.gif)
联立①②③④式求得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843664415.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843680634.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843727558.gif)
圆柱半径为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843758634.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目