题目内容
如图所示,光滑竖直圆环轨道,O为圆心,半径为R,B点与O点等高,在最底点固定一点电荷A,B点恰能静止一质量为m,电荷量为q的带孔小球,现将点电荷A的电量增加为原来的两倍,,小球沿圆环轨道向上运动到最高点C时的速度为
,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328031482551.jpg)
(1)小球在B点刚开始运动时的加速度;
(2)小球在C点时,对轨道的压力
(3)点电荷A的电量增加为原来的两倍后,B、C两点间的电势差
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803117502.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328031482551.jpg)
(1)小球在B点刚开始运动时的加速度;
(2)小球在C点时,对轨道的压力
(3)点电荷A的电量增加为原来的两倍后,B、C两点间的电势差
(1)
,方向竖直向上(2)球对轨道的压力大小为
,方向为竖直向上(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803211808.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803164387.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803179682.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803211808.png)
(1)设点电荷A的电量为Q,受力分析图如图所示
小球在B点静止,则有:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328032261124.png)
当A的电量增加为原来的两倍时,则有![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328032571445.png)
所以,
,方向竖直向上
(2)在C点时,设轨道对球的压力方向向下,大小为N,根据圆周运动知识可![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328033041420.png)
所以,
,
所以,球对轨道的压力大小为
,方向为竖直向上
(3)设B、C两点间电势差为U,
则由动能定理可得
则,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803211808.png)
小球在B点静止,则有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328032261124.png)
当A的电量增加为原来的两倍时,则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328032571445.png)
所以,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803164387.png)
(2)在C点时,设轨道对球的压力方向向下,大小为N,根据圆周运动知识可
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328033041420.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241328034601904.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803491815.png)
所以,球对轨道的压力大小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803179682.png)
(3)设B、C两点间电势差为U,
则由动能定理可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803554977.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132803211808.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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