题目内容
一开口玻璃管竖直放置在小车上,小车沿倾角为37°的光滑斜面下滑.在运动前,玻璃管中有一段h=20cm的水银柱,封闭一段L0=40cm长的空气柱.设大气压强p0=75cm汞柱,温度不变,水银密度为
=13.6×
,g=10m/
.(见图)求小车下滑过程中空气柱长为多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123581689.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412012353495.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123550194.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123565101.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123581689.gif)
43.3cm
水银柱在下滑过程中沿斜面的加速度a=gsin37°
它在竖直方向的分加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123597374.gif)
设玻璃管截面积为S,下滑过程中气体压强为P,水银密度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123612283.gif)
则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123628301.gif)
对空气柱:根据玻一马定律,设后来的长度为L
则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123643296.gif)
解之得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120123659467.gif)
代入数值:L=43.3cm
![](http://thumb2018.1010pic.com/images/loading.gif)
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