题目内容
(12分) 在光滑水平面上静置有质量均为m的木板AB和滑块CD,木板AB上表面粗糙,动摩擦因数为μ,滑块CD上表面为光滑的1/4圆弧,它们紧靠在一起,如图1-93所示.一可视为质点的物块P质量也为m,它从木板AB右端以初速v0滑入,过B点时速度为v0/2,后又滑上滑块,最终恰好滑到最高点C处,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500514086211390.png)
(1)物块滑到B处时,木板的速度vAB;
(2)木板的长度L;
(3)物块滑到C处时滑块CD的动能.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500514086211390.png)
(1)物块滑到B处时,木板的速度vAB;
(2)木板的长度L;
(3)物块滑到C处时滑块CD的动能.
(1)
;(2)
;(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005140924806.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005140877449.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005140893791.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005140924806.png)
试题分析:(1)物体由A滑至B的过程中,由三者系统水平方向动量守恒得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051409401015.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005140955652.png)
(2)物块由A滑至B的过程中,由三者功能关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051410021763.png)
解之得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005141018898.png)
(3)物块由D滑到C的过程中,二者系统水平方向动量守恒,又因为物块到达最高点C时,物块与滑块速度相等且水平,均为v.
故得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005141033951.png)
∴ 得滑块的动能
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051410651250.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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