题目内容
雨伞边缘的半径为r,距水平地面的高度为h,现将雨伞以角速度ω匀速旋转,使雨滴自伞边缘甩出,落在地面上成一个大圆圈。求:(1)大圆圈的半径是多少? (2)雨滴落到地面时速率是多少?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843274754.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843274754.gif)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843290823.gif)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843305577.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843290823.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843305577.gif)
(1)∵雨滴离开雨伞的速度为
,雨滴做平抛运动的时间为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843337508.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843352881.gif)
∴雨滴的水平位移为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843368666.gif)
∴雨滴落在地上形成的大圆的半径为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843290823.gif)
(2)设雨滴落地时的速率为v,根据机械能守恒定律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843399735.gif)
解得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843305387.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843337508.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843352881.gif)
∴雨滴的水平位移为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843368666.gif)
∴雨滴落在地上形成的大圆的半径为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843290823.gif)
(2)设雨滴落地时的速率为v,根据机械能守恒定律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843399735.gif)
解得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113843305577.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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