题目内容
一细棒处于磁感应强度为B的匀强磁场中,棒与磁场方向垂直,与水平方向夹角为
。磁感线水平指向纸里,如图所示,棒上套一个可在其上滑动的带负电的小球C,小球质量为m,带电量为q,球与棒间的动摩擦因数为
,让小球从棒上端静止下滑,求:
(1)小球的最大速度;
(2)动摩擦因数应具备的条件。
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/20110601133732670885.gif)
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/20110601133732685883.gif)
(1)小球的最大速度;
(2)动摩擦因数应具备的条件。
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337327012581.gif)
解:(1)小球速度最大时,棒对它的弹力垂直于棒向下,沿杆方向,
,
垂直杆方向:
,
联立以上各式,得![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337327321598.gif)
所以:![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337327481620.gif)
(2)小球C从斜置的绝缘棒上由静止开始运动,必须满足条件
,
而![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337328101243.gif)
即
,
所以
。
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337327011153.gif)
垂直杆方向:
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337327161382.gif)
联立以上各式,得
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337327321598.gif)
所以:
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337327481620.gif)
(2)小球C从斜置的绝缘棒上由静止开始运动,必须满足条件
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337327791213.gif)
而
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337328101243.gif)
即
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337328101385.gif)
所以
![](http://thumb.1010pic.com/pic1/upload/papers/g04/20110601/201106011337328261070.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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