电磁刹车技术的应用越来越广泛。某电磁刹车装置可简化为如图甲所示的模型,车厢下端固定有电磁铁系统,能在长为L
1、宽为L
2的矩形区域内产生竖直方向的匀强磁场,磁感应强度的大小可根据需要自动调整,但最大不超过2T。长为L
1、宽为L
2的单匝矩形线圈铺设在水平绝缘轨道正中央,相邻两线圈的间隔也为L
2。已知
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.5%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.2%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 每个线圈的电阻
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.1%3C%2Fmn%3E%3Cmtext%3E%CE%A9%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
。在某次试验中,当车的速度
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E20%3C%2Fmn%3E%3Cmtext%3Em%2Fs%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
时启动该制动系统,车立即以大小为2m/s
2的加速度做匀减速直线运动,直到磁感应强度达到2T。之后磁感应强度保持2T不变,车继续前行直到停止运动。已知车的总质量为30kg,不计摩擦阻力及空气阻力的影响,导线粗细忽略不计,不考虑磁场边缘效应的影响。
![](http://tikupic.21cnjy.com/2023/01/10/00/0d/000d0b9ecc1f7168df03408f826715e3_576x160.png)