题目内容
如图所示,两电阻不计的足够长光滑平行金属导轨与水平面夹角
,导轨间距
,所在平面的正方形区域abcd内存在有界匀强磁场,磁感应强度为
T,方向垂直斜面向上。将甲乙两电阻阻值相同、质量均为
kg的相同金属杆如图放置在导轨上,甲金属杆处在磁场的上边界,甲乙相距也为
,其中
m。静止释放两金属杆的同时,在甲金属杆上施加一个沿着导轨的外力F,使甲金属杆在运动过程中始终做沿导轨向下的匀加速直线运动,加速度大小5m/s2,乙金属杆刚进入磁场时即作匀速运动。(取
m/s2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241603011084249.png)
(1)求金属杆甲的电阻R;
(2)以刚释放时
,写出从开始到甲金属杆离开磁场,外力F随时间t的变化关系;
(3)若从开始释放到乙金属杆离开磁场,乙金属杆中共产生热量
J,试求此过程中外力F对甲做的功。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160259641437.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160259813250.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160300000447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160300250499.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160259813250.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160300702404.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160300905404.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241603011084249.png)
(1)求金属杆甲的电阻R;
(2)以刚释放时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160301186335.png)
(3)若从开始释放到乙金属杆离开磁场,乙金属杆中共产生热量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160301388536.png)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160301591534.png)
(2)
(N)
(3) WF="2/75J" =0.0266J
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160301591534.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160301810561.png)
(3) WF="2/75J" =0.0266J
试题分析:(1)因为甲、乙加速度相同,所以,当乙进入磁场时,甲刚出磁场
乙进入磁场时的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160302012758.png)
根据平衡条件有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241603021221065.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241603022461629.png)
(2)甲在磁场中运动时,外力F始终等于安培力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160302371808.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160302465644.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241603025581319.png)
(3)乙进入磁场前,甲、乙发出相同热量,设为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160302683362.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160302792670.png)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160302886467.png)
故外力F对甲做的功
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160302980793.png)
甲出磁场以后,外力F为零
乙在磁场中,甲、乙发出相同热量,设为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160303089383.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160303260702.png)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160303354786.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824160303510546.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241603036501266.png)
点评:本题难度中等,关键是根据回路的构成和导体棒切割磁感线从能量转化角度考虑问题,切割磁感线的那一部分导体相当于电源,克服安培力做功等于焦耳热的产生,利用这些结论求解
![](http://thumb2018.1010pic.com/images/loading.gif)
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