题目内容
如图所示,竖直光滑直轨道OA高度为2R,连接半径为R的半圆形光滑环形管道ABC(B为最低点),其后连接
圆弧环形粗糙管道CD,半径也为R.一个质量为m的小球从O点由静止释放,自由下落至A点进入环形轨道,从D点水平飞出,下落高度刚好为R时,垂直落在倾角为30°的斜面上P点,不计空气阻力,重力加速度为g.求:
(1)小球运动到B点时对轨道的压力大小;
(2)小球运动到D点时的速度大小;
(3)小球在环形轨道中运动时,摩擦力对小球做了多少功?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241401598727358.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159825297.png)
(1)小球运动到B点时对轨道的压力大小;
(2)小球运动到D点时的速度大小;
(3)小球在环形轨道中运动时,摩擦力对小球做了多少功?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241401598727358.png)
(1)N =7mg(2)
(3)-
mgR
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159919554.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159935364.png)
(1)O→B:3mgR=
mυB2
B点:N– mg=m![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140200059500.png)
N ˊ=" N" =7mg
(2)D→P:υy=gt R=
gt2
在P点:
=tan60°
υD=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159919554.png)
(3)O→D:mgR+Wf =
mυD2 Wf =-
mgR
本题综合考查了曲线运动,根据牛顿第二定律可得小球在B点时对轨道的压力,要求小球在D点时的速度,可把运动过程逆过来球,现根据小球做平抛运动的规律求出平抛运动的初速度,即D点的速度从O到D整个过程中只有重力和摩擦力做功,可根据动能定理求得。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159981327.png)
B点:N– mg=m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140200059500.png)
N ˊ=" N" =7mg
(2)D→P:υy=gt R=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159981327.png)
在P点:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140200137474.png)
υD=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159919554.png)
(3)O→D:mgR+Wf =
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159981327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140159935364.png)
本题综合考查了曲线运动,根据牛顿第二定律可得小球在B点时对轨道的压力,要求小球在D点时的速度,可把运动过程逆过来球,现根据小球做平抛运动的规律求出平抛运动的初速度,即D点的速度从O到D整个过程中只有重力和摩擦力做功,可根据动能定理求得。
![](http://thumb2018.1010pic.com/images/loading.gif)
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