题目内容
如图所示,两条足够长的平行光滑导轨MN和PQ之间的宽度为L,处于同一竖直平面内,MP间接有阻值为R的电阻。轻质金属杆ab长为2L,紧贴导轨竖直放置并与导轨接触良好,离a端
处固定有质量为m的小球(可视为质点),整个装置处于磁感应强度为B并与导轨平面垂直的匀强磁场中,当ab杆由静止开始紧贴导轨绕a端固定轴向右倒下至水平位置时,球的速度为v。若导轨及金属杆电阻不计,忽略各处的摩擦,重力加速度为g,则在金属杆b端即将脱离导轨MN的瞬间,求:
(1) 小球的速度大小;
(2) 电阻R的电功率。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241151338695050.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115133853107.gif)
(1) 小球的速度大小;
(2) 电阻R的电功率。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241151338695050.gif)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115133916377.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115133916294.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115133916377.gif)
(1)设b端即将脱离MN时的速度为v0
由题中条件知:b端即将脱离导轨MN时,ab杆与PQ的夹角为300 (2分)
根据机械能守恒:
(5分)
解得:
(2分)
(2)杆与球角速度相同,b端即将脱离导轨MN时杆中点速度
(2分) 感应电动势:
(3分)
功率
(3分) 解得:
(2分)
由题中条件知:b端即将脱离导轨MN时,ab杆与PQ的夹角为300 (2分)
根据机械能守恒:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115133931455.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115133916294.gif)
(2)杆与球角速度相同,b端即将脱离导轨MN时杆中点速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115133978353.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115134025162.gif)
功率
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115134134199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115133916377.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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