题目内容
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203571011854.gif)
如下图所示,粗细均匀的长直玻璃管被轻绳倒挂于倾角为θ的斜面上,管内有一段长为h的水银柱(其密度为ρ)封闭着一段空气柱.求在下列情况下,被封闭气体的压强为多少(式中各物理量单位均为国际单位制单位)?
(1)玻璃管静止不动;
(2)剪断细绳后,玻璃管沿斜面保持平稳加速下降过程(知管与斜面间动摩擦因数为μ,且μ<tanθ).
(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203571171766.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203571321877.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203571321987.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203571482022.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203571632033.gif)
(1)当玻璃管静止时,设被封闭气体的压强为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120357179948.gif)
根据水银柱沿斜面方向受力平衡
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203571951188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203572101159.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203572261295.gif)
(2)在玻璃管沿粗糙斜面匀加速下降过程中,设被封闭气体压强为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120357241951.gif)
①以玻璃管、水银柱及封闭气体整体为研究对象,其受力情况如下图所示.分别沿垂直于斜面和平行于斜面方向应用力的平衡条件和牛顿第二定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203572571411.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203572731141.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203572881336.gif)
②以水银柱为研究对象,其受力情况如下图所示,沿平行于斜面方向应用牛顿第二定律,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203573041250.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203573191411.gif)
将m=ρSh及上面求出的a值代入该式并整理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241203573351191.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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