题目内容
如图1所示,一个质量为m,电量为-q的小物体,可在水平轨道x上运动,O端有一与轨道垂直的固定墙,轨道处在场强大小为E,方向沿Ox轴正向的匀强磁场中,小物体以初速度v0从点x0沿Ox轨道运动,运动中受到大小不变的摩擦力f作用,且f<qE ,小物体与墙壁碰撞时不损失机械能,求它在停止前所通过的总路程?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241216009112735.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241216009112735.jpg)
(1)在A点,小球在水平方向只受电场力作用,根据牛顿第二定律得: ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600927507.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
所以小球在A点的速度
。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
(2)在小球从A到B的过程中,根据动能定理,电场力做的正功等于小球动能的增加量,即
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
小球在B点时,根据牛顿第二定律,在水平方向有![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121601129589.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
解以上两式,小球在B点对环的水平作用力为:
。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600927507.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
所以小球在A点的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121601005563.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
(2)在小球从A到B的过程中,根据动能定理,电场力做的正功等于小球动能的增加量,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121601067732.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
小球在B点时,根据牛顿第二定律,在水平方向有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121601129589.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
解以上两式,小球在B点对环的水平作用力为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121601161462.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600833333.jpg)
![](http://thumb2018.1010pic.com/images/loading.gif)
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