题目内容
如图所示,一个重为G的小环套在竖直放置的半径为R的光滑大圆环上,一个原长为L(L < 2R)的轻弹簧,一端固定在大圆环顶点A,另一端与小环相连,小环在大圆环上可无摩擦滑动.环静止于B点时,弹簧与竖直方向的夹角为θ,试求:
(1)小环在B点时,大圆环对它的支持力FN
(2)该弹簧的劲度系数为k。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500215224116318.png)
(1)小环在B点时,大圆环对它的支持力FN
(2)该弹簧的劲度系数为k。
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152287979.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152256519.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152287979.png)
试题分析:受力分析如下图
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021523036143.jpg)
小球受自身重力
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152319316.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152334411.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152350302.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152365297.png)
根据几何关系可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152256519.png)
根据平行四边形几何关系合力即弹簧弹力
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152397662.png)
根据圆环内的弦长即弹簧长度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152412567.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021524281003.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002152287979.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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