问题 问答题

如图所示,质量M="3.5" kg的小车静止于光滑水平面上靠近桌子处,其上表面与水平桌面相平,小车长L="1.2" m,其左端放有一质量为m2="0.5" kg的滑块Q。水平放置的轻弹簧左端固定,质量为m1="1" kg的小物块P置于桌面上的A点并与弹簧的右端接触。此时弹簧处于原长,现用水平向左的推力将P缓慢推至B点(弹簧仍在弹性限度内)时,推力做的功为WF,撤去推力后,P沿桌面滑动到达C点时的速度为2 m/s,并与小车上的Q相碰,最后Q停在小车的右端,P停在距小车左端S="0.5" m处。已知AB间距L1="5" cm,A点离桌子边沿C点距离L2="90" cm,P与桌面间动摩擦因数μ1=0.4,PQ与小车表面间动摩擦因数μ2=0.1。(g="10" m/s。)求:

(1)推力做的功WF

(2)PQ碰撞后瞬间Q的速度大小和小车最后速度v.

答案

(1) WF="6J                                                                        "

(2) 0.4m/s

(1)对PABC应用动能定理,得

                                                                

解得                                                                                            

(2)设PQ碰后速度分别为v1v2,小车最后速度为v,由动量守恒定律得

m1vc=m1v1+-m2v2                                                                                 

m1vc=(m1+m2+M)v                                                                                

由能量守恒得

                       

解得,v2=2m/s

v2=

v=0.4m/s                                                                                                 

当v2′=时,v1=>v2不合题意,舍去。                            

PQ碰撞后瞬间Q的速度大小为v2=2m/s

小车最后速度为0.4m/s

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