如图所示，质量为m3=3kg的滑道静止在光滑的水平面上，滑道的AB部_爱下问搜题

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问题计算题

如图所示，质量为m₃=3kg的滑道静止在光滑的水平面上，滑道的AB部分是半径为R=0.15m的四分之一的圆弧，圆弧底部与滑道水平部分相切，滑到水平部分右端固定一个轻弹簧。滑道除CD部分粗糙外其他部分均光滑。质量为m₂=2kg的物体2（可视为质点）放在滑道的B点，现让质量为m₁=1kg的物体1（可视为质点）自A点静止释放，两物体在滑道BC之间相碰后并粘为一体（g=10m/s²）。

（1）求物体1从释放到与物体2相碰的过程中，滑道向左运动的距离；

（2）若CD=0.1m，两物体与滑道的CD部分的动摩擦因数都为，求在整个运动过程中，弹簧具有最大弹性势能。

答案

解：（1）m₁从释放到与m₂相碰撞过程，m₁、m₃组成的系统水平方向动量守恒，设m₁水平位移大小s₁，m₃水平位移大小s₃，有

可以求得

（2）设m₁、m₂刚要相碰时物体1的速度v₁，滑道的速度为v₃，由机械能守恒定律有

由动量守恒定律有

设物体1和物体2相碰后的共同速度为v₂，由动量守恒定律有

弹簧第一次压缩最短时由动量守恒定律可知物体1、2和滑道速度为零，此时弹性势能最大，设为E_pm。从物体1、2碰撞后到弹簧第一次压缩最短的过程中，由能量守恒有

联立以上方程，代入数据可得

完形填空

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A．pulled into

问答题简答题

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