题目内容
如图所示,EF为水平地面,O点左侧是粗糙的,右侧是光滑的,一轻质弹簧右端固定在墙壁上,左端与静止在O点、质量为m的小物块A连接,弹簧处于原长状态.质量为2m的物块B在大小为F的水平恒力作用下由C处从静止开始向右运动,已知物块B与地面EO段间的滑动摩擦力大小为
,物块B运动到O点与物块A相碰并一起向右运动(设碰撞时间极短),运动到D点时撤去外力F.物块B和物块A可视为质点.已知CD=5L,OD=L.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144033404147.jpg)
(1)撤去外力后弹簧的最大弹性势能?
(2)物块B从O点开始向左运动直到静
止所用的时间是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403324226.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144033404147.jpg)
(1)撤去外力后弹簧的最大弹性势能?
(2)物块B从O点开始向左运动直到静
止所用的时间是多少?
(1)
;(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403387601.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403371304.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403387601.gif)
(1)设B与A碰撞前速度为v0,由动能定理,得
,则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403434535.gif)
B与A在O点碰撞,设碰后共同速度为v1,
由动量守恒得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403434998.gif)
碰后B和A一起运动,运动到D点时撤去外力F后,当它们的共同速度减小为零时,弹簧的弹性势能最大,设为Epm,则由能量守恒得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403449855.gif)
(2)设A、B一起向左运动回到O点的速度为v2,由机械能守恒得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403465904.gif)
经过O点后,B和A分离,B在滑动摩擦力的作用下做匀减速直线运动,设运动时间为t,由动量定理得
,则
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403402656.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403434535.gif)
B与A在O点碰撞,设碰后共同速度为v1,
由动量守恒得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403434998.gif)
碰后B和A一起运动,运动到D点时撤去外力F后,当它们的共同速度减小为零时,弹簧的弹性势能最大,设为Epm,则由能量守恒得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403449855.gif)
(2)设A、B一起向左运动回到O点的速度为v2,由机械能守恒得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403465904.gif)
经过O点后,B和A分离,B在滑动摩擦力的作用下做匀减速直线运动,设运动时间为t,由动量定理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403496527.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114403605626.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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