题目内容
(2003年全国理综卷)如图5所示,两根平行的金属导轨,固定在同一水平面上,磁感应强度B=0.50T的匀强磁场与导轨所在平面垂直,导轨的电阻很小,可忽略不计。导轨间的距离l=0.20m。两根质量均为m=0.10kg的平行金属杆甲、乙可在导轨上无摩擦地滑动,滑动过程中与导轨保持垂直,每根金属杆的电阻为R=0.50Ω。在t=0时刻,两杆都处于静止状态。现有一与导轨平行、大小为0.20N的恒力F作用于金属杆甲上,使金属杆在导轨上滑动。经过t=5.0s,金属杆甲的加速度为a=1.37m/s2,问此时两金属杆的速度各为多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647577637.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647577637.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647593684.gif)
设任一时刻t两金属杆甲、乙之间的距离为x,速度分别为v1和v2,经过很短的时间△t,杆甲移动距离v1△t,杆乙移动距离v2△t,回路面积改变
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647608933.gif)
由法拉第电磁感应定律,回路中的感应电动势![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647624506.gif)
回路中的电流![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647624430.gif)
杆甲的运动方程![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647639467.gif)
由于作用于杆甲和杆乙的安培力总是大小相等,方向相反,所以两杆的动量
时为0)等于外力F的冲量![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647686494.gif)
联立以上各式解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647717809.gif)
代入数据得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647593684.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647608933.gif)
由法拉第电磁感应定律,回路中的感应电动势
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647624506.gif)
回路中的电流
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647624430.gif)
杆甲的运动方程
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647639467.gif)
由于作用于杆甲和杆乙的安培力总是大小相等,方向相反,所以两杆的动量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647671262.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647686494.gif)
联立以上各式解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647702814.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647717809.gif)
代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114647593684.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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