题目内容
雨滴在空中运动时,受到的空气阻力与其速度的平方成正比.若两个雨滴从空中落下,其质量分别为m1、m2,落至地面前均已做匀速直线运动,则两雨滴落地前时重力的功率之比为________.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120050665374.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120050681381.gif)
根据平衡条件得 mg=kv2,雨滴的收尾速度为v=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120050696414.gif)
则落地时重力对雨滴做功的功率为P=mgv=mg![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120050712403.gif)
所以,两雨滴落地时重力的功率之比为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120050727564.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120050696414.gif)
则落地时重力对雨滴做功的功率为P=mgv=mg
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120050712403.gif)
所以,两雨滴落地时重力的功率之比为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120050727564.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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