题目内容
如图所示,将边长为a、质量为m、电阻为R的正方形导线框竖直向上抛出,穿过宽度为b、磁感应强度为B的匀强磁场,磁场的方向垂直纸面向里.线框向上离开磁场时的速度刚好是进入磁场时速度的一半,线框离开磁场后继续上升一段高度,然后落下并匀速进入磁场.整个运动过程中始终存在着大小恒定的空气阻力f且线框不发生转动.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241210054182597.jpg)
(1)线框在下落阶段匀速进入磁场时的速度v2;
(2)线框在上升阶段刚离开磁场时的速度v1;
(3)线框在上升阶段通过磁场过程中产生的焦耳热Q.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241210054182597.jpg)
(1)线框在下落阶段匀速进入磁场时的速度v2;
(2)线框在上升阶段刚离开磁场时的速度v1;
(3)线框在上升阶段通过磁场过程中产生的焦耳热Q.
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241210054331081.gif)
(3)
m[(mg)2-f2]
-(mg+f)(a+b)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241210054331081.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005449223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005464459.gif)
(1)线框在下落阶段匀速进入磁场瞬间
mg=f+
①
解得v2=
. ②
(2)线框从离开磁场至上升到最高点的过程中
(mg+f)h=
mv12 ③
线框从最高点回落至进入磁场瞬间
(mg-f)h=
mv22 ④
③④联立解得v1=
⑤
(3)线框在向上通过磁场过程中
mv02-
mv12=Q+(mg+f)(a+b)v0=2v1
Q=
m[(mg)2-f2]
-(mg+f)(a+b).
mg=f+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005496481.gif)
解得v2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005511610.gif)
(2)线框从离开磁场至上升到最高点的过程中
(mg+f)h=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005527225.gif)
线框从最高点回落至进入磁场瞬间
(mg-f)h=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005527225.gif)
③④联立解得v1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241210055581076.gif)
(3)线框在向上通过磁场过程中
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005527225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005527225.gif)
Q=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005449223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121005464459.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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