题目内容
(12分)如图所示,一质量
的滑块(可视为质点)从固定的粗糙斜面的顶端由静止开始下滑,滑到斜面底端时速度大小
.已知斜面的倾角
,斜面长度
,
,
,空气阻力忽略不计,重力加速度取
.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250026406382309.png)
(1)滑块沿斜面下滑的加速度大小;
(2)滑块与斜面间的动摩擦因数;
(3)在整个下滑过程中重力对滑块所做功的平均功率。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640467635.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640482625.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640514478.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640529540.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640576649.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640607655.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640623664.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250026406382309.png)
(1)滑块沿斜面下滑的加速度大小;
(2)滑块与斜面间的动摩擦因数;
(3)在整个下滑过程中重力对滑块所做功的平均功率。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640701561.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640670617.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640685459.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640701561.png)
试题分析: (1)滑块在斜面上做匀加速直线运动,由运动学公式:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640716549.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640670617.png)
(2)对滑块受力分析,由牛顿第二定律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640763765.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640779570.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640794779.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640685459.png)
(3)设滑块下滑的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640841267.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640857621.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002640872423.png)
则重力做功的平均功率为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250026409041297.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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