题目内容
如图,质量分别为mA和mB的两小球带有同种电荷,电荷最分别为qA和qB,用绝缘细线悬挂在天花板上。平衡时,两小球恰处于同一水平位置,细线与竖直方向间夹角分别为θ1与θ2(θ1>θ2)。两小球突然失去各自所带电荷后开始摆动,最大速度分别vA和vB,最大动能分别为EkA和EkB。则 ( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241346420452229.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241346420452229.png)
A.mA一定小于mB | B.qA一定大于qB |
C.vA一定大于vB | D.EkA一定大于EkB |
ACD
分别对A、B进行受力分析,如图所示
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241346420764572.jpg)
两球间的库仑斥力是作用力与反作用力总是大小相等,与带电量的大小无关,因此B选项不对,
对于A球:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642138821.png)
对于B球:
联立得:F=
又θ1>θ2可以得出:mA<mB A选项正确
在两球下摆的过程中根据机械能守恒:
可得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642403963.png)
可得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642559967.png)
开始A、B两球在同一水平面上,
由于θ1>θ2可以得出:LA>LB
这样代入后可知:
C选项正确
A到达最低点的动能:
B到达最低点的动能:
由于θ1>θ2可知,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642887790.png)
又:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642622729.png)
可得:
因此D选项也正确。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241346420764572.jpg)
两球间的库仑斥力是作用力与反作用力总是大小相等,与带电量的大小无关,因此B选项不对,
对于A球:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642107661.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642138821.png)
对于B球:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642185669.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642216842.png)
联立得:F=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642294987.png)
在两球下摆的过程中根据机械能守恒:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241346423411248.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642403963.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241346424971248.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642559967.png)
开始A、B两球在同一水平面上,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642622729.png)
由于θ1>θ2可以得出:LA>LB
这样代入后可知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642700493.png)
A到达最低点的动能:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241346427933900.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241346428403996.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642887790.png)
又:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134642622729.png)
可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134643012969.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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