如图所示,MPQ、M′P′Q′是光滑平行导轨,其中倾斜部分MPP′M′为金属材料制成,电阻可不计,倾角为α=37°,并处在与MPP′M′平面垂直且向下的匀强磁场中(图中未画出),磁感应强度大小为2T;水平部分PQQ′P′为绝缘材料制成,所在空间内存在竖直方向的磁场,在PQ上取一点为坐标原点O,沿PQ方向建立x轴,可知磁感应强度分布规律为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmtext%3ET%3C%2Fmtext%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3C%2Fmtd%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmtext%3ET%3C%2Fmtext%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3C%2Fmtd%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(取竖直向上为正方向);两部分导轨的衔接处用小圆弧连接,金属棒通过时无机械能损失,两导轨间接有阻值为R=5Ω的定值电阻。正方形金属线框cdef的质量m
2=2kg、边长为L=1m,每条边的电阻r
2=2Ω,f点刚好位于坐标原点,fc边与PP′平行。现将一根质量m
1=1kg,长度L=1m,电阻r
1=2Ω的金属棒ab从图示位置静止释放,滑到斜面底端前已达到匀速运动。若整个过程ab棒、金属框与导轨始终接触良好,(重力加速度g=10m/s
2 ,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmn%3Ei%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3Ec%3C%2Fmn%3E%3Cmn%3Eo%3C%2Fmn%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3C%2Fmath%3E)
),求:
![](http://tikupic.21cnjy.com/2021/12/31/5e/06/5e06a8f2b9cea865c057b9708354b329_422x176.png)