题目内容
如图12-14所示,不计电阻的U形导轨水平放置,导轨宽
,左端连接阻值为0.4W的电阻R,在导轨上垂直于导轨放一电阻为0.1W的导体棒MN,并用水平轻绳通过定滑轮吊着质量为m=2.4g的重物,图中
,开始重物与水平地面接触并处于静止,整个装置处于竖直向上的匀强磁场中,磁感强度
,并且
的规律在增大,不计摩擦阻力,求至少经过多长时间才能将重物吊起?(
)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139495284121.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949434363.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949450413.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949465334.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949496617.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949512471.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139495284121.jpg)
t=1s
根据题意可知:开始导体棒没有运动时U形导轨和导体棒所构成的闭合回路的面积保持不变,而磁感应强度B在增大,由法拉第电磁感应定律得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139495431074.gif)
而磁场的磁感应强度的变化规律![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949559844.gif)
要把重物吊起来,则绳子的拉力必须大于或等于重力.
设经过时间t重物被吊起,此时磁感应强度为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949606580.gif)
所以安培力为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139496211930.gif)
根据平衡条件得:
解得:t=1s
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139495431074.gif)
而磁场的磁感应强度的变化规律
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949559844.gif)
要把重物吊起来,则绳子的拉力必须大于或等于重力.
设经过时间t重物被吊起,此时磁感应强度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949606580.gif)
所以安培力为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139496211930.gif)
根据平衡条件得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113949637738.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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