题目内容
如图所示,一半径r=1m的圆盘水平放置,在其边缘 E点固定一小桶(可视为质点)。在圆盘直径 DE 的正上方平行放置一水平滑道BC ,滑道右端 C点 与圆盘圆心O在同一竖直线上,且竖直高度h =" 1.25" m。AB为一竖直面内的光滑四分之一圆弧轨道,半径R=0.45m,且与水平滑道相切与B点。一质量m=0.2kg的滑块(可视为质点)从A点由静止释放,当滑块经过C点时,圆盘从图示位置以一定的角速度ω绕通过圆心的竖直轴匀速转动,最终物块由C 点水平抛出,恰好落入圆盘边缘的小桶内.已知滑块与滑道 BC间的摩擦因数μ=0.2。(取g=10m/s2)求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242241378227358.png)
(1)滑块到达B点时受到的支持力NB的大小;
(2)水平滑道 BC的长度L;
(3)圆盘转动的角速度ω应满足的条件。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242241378227358.png)
(1)滑块到达B点时受到的支持力NB的大小;
(2)水平滑道 BC的长度L;
(3)圆盘转动的角速度ω应满足的条件。
(1)6N (2)1.25m (3) ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224139023883.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224139023883.png)
试题分析:(1)沿光滑的四分之一圆弧从A点滑到B点的过程中,只有重力做功,根据动能定理
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224140396924.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224141737657.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224142673961.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224143641789.png)
(2)从C点离开水平轨道后做平抛运动,竖直方向自由落体运动高度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224144109650.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224144935470.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224146183479.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224146433609.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242241469011013.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224147775580.png)
(3)当滑块经过C点时,小圆桶刚好在平抛轨迹上,要使物块恰好落在圆桶内,那么平抛的时间刚好是整数倍个周期,也就是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242241482271201.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224139023883.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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