题目内容
一绝缘楔形物体固定在水平面上,左右两斜面与水平面的夹角分别为
和
,
=37°,
=53°。如图所示,现把两根质量均为m、电阻为均R、长度均为L的金属棒的两端用等长的电阻不计的细软导线连接起来,并把两棒分别放在楔形体的两个光滑的斜面上,在整个楔形体的区域内存在方向竖直向上、磁感应强度为B的匀强磁场,在细软导线刚好拉直后由静止释放两金属棒,不计一切摩擦阻力,细软导线足够长,两导线一直在斜面上,
,
,重力加速度为g。
(1)求金属棒的最大加速度;
(2)求金属棒的最大速度。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241241315705253.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131476188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131492201.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131476188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131492201.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131539425.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131554420.gif)
(1)求金属棒的最大加速度;
(2)求金属棒的最大速度。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241241315705253.jpg)
(1)
a=0.1g
(2)棒受力平衡时,两棒速度v最大。因两棒速度大小相等,但切割B的有效速度不同,感应电流的方向为逆时针
则在 t 时间内感应电动势
其感应电流I=E/2R
安培力Fb=IBL
设细线对棒的力为F
,对右棒:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131820629.gif)
对左棒:
联立解:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131586609.gif)
a=0.1g
(2)棒受力平衡时,两棒速度v最大。因两棒速度大小相等,但切割B的有效速度不同,感应电流的方向为逆时针
则在 t 时间内感应电动势
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131788639.gif)
其感应电流I=E/2R
安培力Fb=IBL
设细线对棒的力为F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412413180485.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131820629.gif)
对左棒:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131835593.gif)
联立解:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124131851510.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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