问题 问答题

如图所示,在水平桌面上放有长木板CC上右端是固定挡板P,在C上左端和中点处各放有小物块ABAB的尺寸以及P的厚度皆可忽略不计,AB之间和BP之间的距离都为L.设木板C和桌面之间无摩擦,ACBC之间的动摩擦因数都为μ,最大静摩擦力等于滑动摩擦力大小,ABC(连同挡板P)的质量都为m,开始时,BC静止,A以某一初速度v0向右运动.求:

(1)AB发生碰撞前,B受到的摩擦力大小;

(2)AB能够发生碰撞时,A的初速度v0应满足的条件;

(3)BP能够发生碰撞时,A的初速度v0应满足的条件(已知AB碰撞前后交换速度).

答案

(1);(2);(3)

(1)设BC无相对滑动,B受到的摩擦力大小为f,则

C,有;对B,有

由以上两式解得,它小于最大静摩擦力,可见BC不发生相对运动.

所以AB发生碰撞前,B受到的摩擦力大小

(2)AC上滑动时,A向右做匀减速运动,BC以相同的加速度向右做匀加速运动.若A运动到B所在位置时,AB刚好不发生碰撞,则ABC速度相同.设三者共同速度为v1,根据动量守恒定律,有

在此过程中,根据功能关系,有

由以上两式解得

所以,AB能够发生碰撞时,A的初速度v0向应满足的条件为

(3)AB碰撞前后交换速度,碰后AC一起向右做匀加速运动、B向右做匀减速运动.若BP刚好不发生碰撞时,B运动到P所在位置ABC速度相同,设三者共同速度为v2,根据动量守恒定律,有

在此过程中,根据功能关系,有

由以上两式解得

所以,BP能够发生碰撞时,A的初速度v0应满足的条件为

阅读理解


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填空题