题目内容
宇航员在月球表面完成下面实验:如图所示,在一固定的竖直光滑圆弧轨道内侧最低点有一小球(可视为质点),当给小球一个水平方向的初速度
时,小球刚好能在竖直面内做完整的圆周运动.已知圆弧轨道半径为r,月球的半径为R,引力常量为G.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241330444682033.jpg)
(1)若在月球表面发射一颗环月卫星,所需最小发射速度为多少?
(2)月球的平均密度为多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044406332.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241330444682033.jpg)
(1)若在月球表面发射一颗环月卫星,所需最小发射速度为多少?
(2)月球的平均密度为多大?
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044515891.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044468641.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044515891.png)
(1)小球恰能在竖直面内做完整的圆周运动,则在其最高点有:
……………………(2分)
小球从轨道最低点到最高点,有:
……………………(2分)
可得,月球表面重力加速度为:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044624654.png)
环月卫星的最小发射速度:
…………(3分)
(2)
……………………(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241330447641026.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044796810.png)
……………………(3分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044546736.png)
小球从轨道最低点到最高点,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241330445771076.png)
可得,月球表面重力加速度为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044624654.png)
环月卫星的最小发射速度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044640752.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044686962.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044733873.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241330447641026.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044796810.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133044842951.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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