题目内容
(16分)足够长的光滑平行金属导轨
和
水平放置,在其左端固定一个倾角为
的光滑金属导轨,导轨相距均为
,在水平导轨和倾斜导轨上,各有一根与导轨垂直的金属杆,两金属杆与水平导轨、倾斜导轨形成—闭合回路。两金属杆质量均为
、电阻均为
,其余电阻不计,杆
被销钉固定在倾斜导轨某处。整个装置处于匀强磁场中,磁感应强度为
,方向竖直向上。当用水平向右、大小
的恒力拉杆
,使其达到最大速度时,立即撤去销钉,发现杆
恰好能在原处仍然保持静止。(重力加速度为
)
(1)求杆
运动中的最大速度
。
(2)求倾斜导轨的倾角
。
(3)若杆
加速过程中发生的位移为
,则杆
加速过程中,求杆
上产生的热量
。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215071225480.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506826221.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506841227.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506857200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506857419.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506872455.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506888320.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506904197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506935266.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506935458.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506950192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506904197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506982471.gif)
(1)求杆
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506950192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507013185.gif)
(2)求倾斜导轨的倾角
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506857200.gif)
(3)若杆
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506950192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507060367.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506950192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121506904197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507106233.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215071225480.jpg)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507138474.gif)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507153300.gif)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507169511.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507138474.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507153300.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507169511.gif)
(1)对杆a,匀速运动时:
(2分)
杆a产生的电动势
(2分)
回路电流
(2分)解得:
(2分)
(2)对杆b:
解得:
(2分)
(3)对系统,由能量守恒定律得:
(2分)
(2分)解得:
(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507184563.gif)
杆a产生的电动势
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507200302.gif)
回路电流
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507216323.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507216818.gif)
(2)对杆b:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507247561.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507153300.gif)
(3)对系统,由能量守恒定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507262679.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121507278417.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215072941195.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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