题目内容
(20分)光滑水平面上有一质量为M="2" kg的足够长的木板,木板上最右端有一大小可忽略、质量为m=3kg的物块,物块与木板间的动摩擦因数
,且最大静摩擦力等于滑动摩擦力。开始时物块和木板都静止,距木板左端L=2.4m处有一固定在水平面上的竖直弹性挡板P。现对物块施加一水平向左外力F=6N,若木板与挡板P发生撞击时间极短,并且搏击时无动能损失,物块始终未能与挡板相撞,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029481352659.jpg)
(1)木板第一次撞击挡板P时的速度
为多少?
(2)木板从第一次撞击挡板P到运动到右端最远处所需的时间
及此时物块距木板右端的距离X为多少?
(3)木板与挡板P会发生多次撞击直至静止,而物块一直向左运动。每次木板与挡板p撞击前物块和木板都已相对静止,最后木板静止于挡板P处,求木板与物块都静止时物块距木板有端的距离X为多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948104449.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029481352659.jpg)
(1)木板第一次撞击挡板P时的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948322265.png)
(2)木板从第一次撞击挡板P到运动到右端最远处所需的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948338291.png)
(3)木板与挡板P会发生多次撞击直至静止,而物块一直向左运动。每次木板与挡板p撞击前物块和木板都已相对静止,最后木板静止于挡板P处,求木板与物块都静止时物块距木板有端的距离X为多少?
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948416453.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948354585.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948369391.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948400486.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948416453.png)
试题分析:(1)设木板靠最大静摩擦力或滑动摩擦力产生的加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948432382.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029484471094.png)
若木板与物块不发生相对运动,设共同加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948478315.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029484941040.png)
因
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948510441.png)
根据运动学公式
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948525521.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948354585.png)
(2)设木板第一次撞击挡板P后向右运动时,此时木板和物块之间摩擦力变为滑动摩擦力。
物块的加速度大小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948572344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948588763.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948603601.png)
木板则以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948432382.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948650465.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948666770.png)
设木板左端距挡板P的距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948681349.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029487121040.png)
设物块相对地向左的位移为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948728374.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029487441036.png)
此时物块距木板右端的距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948806769.png)
(3)木板最终静止于挡板P处,设物块距木板右端的距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948822376.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948837978.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002948853614.png)
评分参考:第(1)问5分,①②③④⑤式各1分;第(2)问10分,其中⑥式2分,⑦式1分,⑧⑨⑩式各2分,⑾式1分;第(3)问5分,⑿式3分,⒀式2分。
![](http://thumb2018.1010pic.com/images/loading.gif)
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