题目内容
如图所示,在水平向右的的匀强电场中,长为l的绝缘轻杆可绕固定轴O在竖直面内无摩擦转动,两个小球A、B固定于杆的两端,A、B的质量分别为m和2m,A带负电,电量为q,B带正电,电量也为q。若杆在水平位置,由静止开始转动,杆能转过的最大角度为60°,则匀强电场的场强E=_________,在杆转动的过程中两球各自能达到的最大速度v=__________。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241308153152510.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241308153152510.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815378709.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815424733.png)
由开始转动到最大角度的过程:由动能定理有:
2mg
sin60°-mg
sin60°-Eq
(1-cos60°)-Eq
(1-cos60°)=0
解得,E=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815378709.png)
此运动类似单摆,关于等效平衡位置对称:从初始位置到最大速度的过程有:
2mg
sin30°-mg
sin30°-Eq
(1-cos30°)-Eq
(1-cos30°)=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815986719.png)
解得:v=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815424733.png)
2mg
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815471398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815471398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815471398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815471398.png)
解得,E=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815378709.png)
此运动类似单摆,关于等效平衡位置对称:从初始位置到最大速度的过程有:
2mg
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815471398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815471398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815471398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815471398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815986719.png)
解得:v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130815424733.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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