题目内容
三根不可伸长的相同的轻绳,一端系在半径为r0的环1上,彼此间距相等,绳穿过半径为r0的第2个圆环,另一端同样地系在半径为2r0的环3上,如图所示,环1固定在水平面上,整个系统处于平衡状态.试求第2个环中心与第3个环中心之间的距
离.(三个环都是用相同
的金属丝制作的,摩擦不计)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220126955360.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412201266472.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412201268065.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220126955360.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122012711514.gif)
过中心作一截面图,如图所示,由于对称,每根绳上张力相同,设为F.设环2的质量为m,则环3的质量为2m.对环2和3整体有:3F =" mg" + 2mg对环3有:3Fsinθ= 2mg
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220127272469.jpg)
由以上两式得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122012742467.gif)
即
,所以
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220127272469.jpg)
由以上两式得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122012742467.gif)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122012758586.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122012711514.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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