题目内容
有人利用安装在气球载人舱内的单摆来确定气球的高度.已知该单摆在海平面处的周期是T0.当气球停在某一高度时,测得该单摆周期为T.求该气球此时离海平面的高度h.把地球看作质量均匀分布的半径为R的球体.
h=(
-1)R
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441084430.png)
根据单摆周期公式
T0=2π![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441131534.png)
T="2π"![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441162475.png)
其中l是单摆长度,g0和g分别是两地点的重力加速度.根据万有引力公式得
g0=G![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441209576.png)
g=G![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441287806.png)
其中G是引力常数,M是地球质量.由以上各式解得
h=(
-1)R.
T0=2π
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441131534.png)
T="2π"
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441162475.png)
其中l是单摆长度,g0和g分别是两地点的重力加速度.根据万有引力公式得
g0=G
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441209576.png)
g=G
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441287806.png)
其中G是引力常数,M是地球质量.由以上各式解得
h=(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142441084430.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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