题目内容
(12分)如图所示,质量为m的金属小球置于是1/4光滑圆弧顶端的A处无初速度释放。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241217483954180.jpg)
(1)小球落至圆弧最低点B时的速度多大?
(2)此时圆弧B点受到的压力多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241217483954180.jpg)
(1)小球落至圆弧最低点B时的速度多大?
(2)此时圆弧B点受到的压力多大?
解:(1)
(2) 3 mg
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121748411349.gif)
(2) 3 mg
解:(1) 球从A点至最低点过程机械能守恒,设落至最低点时速度为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121748426185.gif)
应有
(3分)
(3分)
(2) 最低点时小球所受支持力N:
(3分)
得:
(2分)
由牛顿第三定律可知,B点所受压力大小为3 mg (1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121748426185.gif)
应有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121748442555.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121748411349.gif)
(2) 最低点时小球所受支持力N:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121748536571.gif)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121748536431.gif)
由牛顿第三定律可知,B点所受压力大小为3 mg (1分)
![](http://thumb2018.1010pic.com/images/loading.gif)
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