题目内容
地球的两颗人造卫星质量之比m1∶m2=1∶2,轨道半径之比r1∶r2=1∶2.求:
(1)线速度大小之比.
(2)角速度之比.
(3)运行周期之比.
(4)向心力大小之比.
(1)线速度大小之比.
(2)角速度之比.
(3)运行周期之比.
(4)向心力大小之比.
(1)
∶1 (2)2
∶1 (3)1∶2
(4)2∶1
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717291344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717291344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717291344.png)
(1)由
=m
,得v=
,
所以
=
=
.
(2)由
=mω2r,得ω= ![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717463689.png)
所以
=
=
.
(3)
=
·
=
=
.
(4)同理
=
=
·
=
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717338626.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717353424.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717369635.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717385406.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717400482.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717416398.png)
(2)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717338626.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717463689.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717478460.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717494603.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717509448.png)
(3)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717525453.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717541532.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717556547.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717556461.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717572438.png)
(4)同理
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717587451.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717603640.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717619338.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717634441.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140825/20140825003717650345.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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