题目内容
两根平行金属
导轨放置在倾角为θ的绝缘斜面上,两导轨间距L,仅在虚线MN下面的空间存在着磁感应强度随高度变化的磁场(在同一水平线上各处磁感应强度相同),磁场方向垂直斜面向下,导轨上端跨接一定值电阻R。质量为m的金属棒两端各套在导轨上并可在导轨上无摩擦滑动,金属棒始终与导轨垂直,导轨和金属棒的电阻不计,现将金属棒从O处由静止释放,进入磁场后正好做匀减速运动,刚进入磁场时速度为v,到达P处时速度为0.5v,O点和P点到MN的距离相等,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241235040195671.jpg)
(1)金属棒在磁场中所受安培力F1的大小;
(2)在金属棒从开始运动到P处的过程中,电阻R上共产生多少热量?
(3)在导轨平面内距MN距离为x处的磁感应强度BX;
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412350398785.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241235040195671.jpg)
(1)金属棒在磁场中所受安培力F1的大小;
(2)在金属棒从开始运动到P处的过程中,电阻R上共产生多少热量?
(3)在导轨平面内距MN距离为x处的磁感应强度BX;
解:(1)设O点和P点到MN的间距均为s,从O→MN过程中棒做匀加速运动,
根据动能定理
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504034694.gif)
从MN→P的过程中做匀减速运动,安培力的大小不变设为F1,根据动能定理
得
(2)解1:棒从MN→P过程中根据能量守恒
得:
解2:棒从MN→P过程中克服安培力做功即为电阻R上产热
(3)设在磁场中运动距离x后速度为vx,对应磁场大小为BX
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412350405073.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412350405073.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412350405073.gif)
解得
根据动能定理
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504034694.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412350405073.gif)
从MN→P的过程中做匀减速运动,安培力的大小不变设为F1,根据动能定理
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504081979.gif)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504097604.gif)
(2)解1:棒从MN→P过程中根据能量守恒
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504112966.gif)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504143502.gif)
解2:棒从MN→P过程中克服安培力做功即为电阻R上产热
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504143314.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504143502.gif)
(3)设在磁场中运动距离x后速度为vx,对应磁场大小为BX
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412350405073.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412350405073.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412350405073.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123504206721.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241235042211085.gif)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241235042841179.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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