题目内容
(16分)如图所示,平板A长
m,质量
kg,放在光滑的水平面上.在A上最右端放一物块B(大小可忽略),其质量m=2kg.已知A、B间动摩擦因数
,开始时A、B都处于静止状态(取
).则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001405987883.png)
(1)若加在平板A上的水平恒力
时,平板A与物块B的加速度大小各为多少?
(2)要将A从物块B下抽出来,则加在平板A上的水平恒力
至少为多大?
(3)若加在平板A上的水平恒力
时,要使物块B从平板A上掉下来
至少作用多长时间?
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001405722410.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001405800471.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001405831449.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001405847657.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001405987883.png)
(1)若加在平板A上的水平恒力
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406127531.png)
(2)要将A从物块B下抽出来,则加在平板A上的水平恒力
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406143302.png)
(3)若加在平板A上的水平恒力
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406159566.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406143302.png)
(1)
(2)
(3) ![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406221506.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406190742.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406205598.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406221506.png)
试题分析:(1)对系统,假设AB之间不发生滑动,则:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406237781.png)
可得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406268605.png)
对B:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406283599.png)
所以假设成立
平板A与物体B的加速度大小为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406190742.png)
(2)要将A从物体B下抽出来,则A与B之间发生相对滑动
对B:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406315647.png)
得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406330675.png)
对系统:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406346825.png)
得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406377576.png)
所以加在平板上的水平恒力至少为24N。
(3)对B:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406393761.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406408918.png)
对A:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406439521.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406455822.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406471652.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406502748.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406517995.png)
又因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406533514.png)
解得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825001406221506.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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