题目内容
(14分)如图甲所示,电阻不计的“
”形光滑导体框架水平放置,导体框处在竖直向上的匀强磁场中,磁感应强度为B=1T,有一导体棒AC横放在框架上且与导体框架接触良好,其质量为m=0.2kg,电阻为R=0.8
,现用绝缘轻绳拴住导体棒,轻绳的右端通过光滑的定滑轮绕在电动机的转轴上,左端通过另一光滑的定滑轮与物体D相连,物体D的质量为M=0.2kg,电动机内阻r=1
。接通电路后电压表的读数恒为U=10V,电流表读数恒为I=1A,电动机牵引原来静止的导体棒AC平行于EF向右运动,其运动位移x随时间t变化的图象如图乙所示,其中OM段为曲线,MN段为直线。(取g=10m/s2)求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029568098268.jpg)
(1)电动机的输出功率;
(2)导体框架的宽度;
(3)导体棒在变速运动阶段产生的热量。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956746462.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956762336.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956762336.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029568098268.jpg)
(1)电动机的输出功率;
(2)导体框架的宽度;
(3)导体棒在变速运动阶段产生的热量。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956856507.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956824416.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956840467.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956856507.png)
试题分析:(1)电动机为非纯电阻电路,电动机总功率
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956871843.png)
电动机内阻发热的功率
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029568871131.png)
那么电动机输出的机械功率
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956902802.png)
(2)位移时间图像的斜率代表速度,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956902378.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956918874.png)
设导轨宽度为L,则有导体棒切割磁感线产生感应电流
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956934606.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956949860.png)
拉动导体棒匀速运动的拉力
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029569961141.png)
根据电动机输出功率有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029570271501.png)
计算得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956840467.png)
(3)根据位移时间图像可知,变速阶段初始度为0,末速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956918874.png)
此过程电动机做功转化为D的重力势能以及D和导体棒的动能还有克服安培力做功即焦耳热。
所以有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029570741428.png)
其中
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002957090589.png)
带入计算得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002956856507.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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