题目内容
如图16所示,在倾角为θ =" 37o" 的斜面的底端有一个固定挡板D,已知物块与斜面PO间的动摩擦因数μ=0.50,斜面OD部分光滑。轻质弹簧一端固定在D点,当弹簧处于自然长度时,另一端在O点;PO = l。在P点有一小物体A,使A从静止开始下滑, A的质量是m,重力加速度为g。求
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241240531323003.png)
(1)弹簧第一次恢复到原长时物体的速度的大小;
(2)物体与弹簧接触多少次后,物体从O点上升的高度小于![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053163534.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241240531323003.png)
(1)弹簧第一次恢复到原长时物体的速度的大小;
(2)物体与弹簧接触多少次后,物体从O点上升的高度小于
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053163534.png)
(1)
;(2)4次。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053194440.png)
本题考查的是牛顿第二定律和功能关系
步骤:物体下滑时加速度
,物体上滑时
,物体第一次下滑到o点到弹簧第一次恢复到原长时,弹簧没有做功,设弹簧第一次恢复到原长时物体的速度的大小为v,根据牛顿第二定律有
,得v=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053194440.png)
(2)设物体第一次返回时沿斜面上升的高度为
,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053459798.png)
即每次沿斜面上升的高度是上一次的
。则第n次上升的高度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053522842.png)
因为
,所以![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053662388.png)
步骤:物体下滑时加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241240532101122.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241240533031157.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053366553.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053194440.png)
(2)设物体第一次返回时沿斜面上升的高度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053428314.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053444607.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053459798.png)
即每次沿斜面上升的高度是上一次的
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053490308.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053522842.png)
因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053646668.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124053662388.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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