过山车是一项好玩又刺激的游乐项目,某挑战者特制了一双能在过山车轨道上滑行的轮滑鞋完成一项挑战运动,挑战者连同装备总质量为m=68kg。过山车轨道示意图如图所示。竖直圆轨道的最低点B与
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
略微错开,它们分别平滑连接弯曲轨道AB与水平轨道
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
。其中圆轨道
![](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%3Cmi%3EC%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
半径R=5.0m,水平轨道
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
长L=40m。在
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
段挑战者利用减速装置可产生大小为总重力0.2倍的摩擦阻力,其余部分摩擦不计。挑战者从P点静止滑下,通过最高点时轨道对轮滑鞋恰好无压力,然后从D点脱离轨道水平飞出,落入水池中央的安全气垫内挑战成功。挑战者可视为质点,空气阻力不计,g取10m/s
2。求:
![](http://tikupic.21cnjy.com/2022/03/07/5d/41/5d41041028548e65b27c831f1249820f_536x182.png)