某中学在开展趣味运动会,同学们每人推出一个滑块,使其沿水平面滑动,娱乐场地如图所示。粗糙的轨道右侧有一半径为
![](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%3E1%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的圆,O为圆心,同学甲首先投掷一个滑块1,结果该滑块1刚好停在中心线与圆的交点B处,同学乙手持另一质量完全相同的滑块2使其沿中心线运动,在合适的位置松开滑块2,经
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的时间两滑块发生正碰。已知同学乙松开滑块2瞬间的速度大小为
![](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%3E14%3C%2Fmn%3E%3Cmrow%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 两滑块碰前
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
内滑块2的位移为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E6.5%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 碰撞过程损失的机械能为碰前滑块2动能的
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 且碰后滑块1、2的速度之比为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E%3A%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 重力加速度g取
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E10%3C%2Fmn%3E%3Cmrow%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmrow%3E%3Cmsup%3E%3Cmtext%3Es%3C%2Fmtext%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 两滑块与轨道间的动摩擦因数相同,最终距离圆心O较近的滑块取得胜利。求:
(1)滑块与轨道之间的动摩擦因数以及松开滑块2瞬间,两滑块之间的距离;
(2)本次游戏,哪位同学取得胜利?
![](http://tikupic.21cnjy.com/ct20241o/c8/1c/c81c0d097a2ca4d738032238e6c0fe3d.png)