题目内容
如图所示,两绳系一质量为0.1 kg的小球,两绳的另一端分别 固定于轴的A、B两处,上面绳长2 m,两绳拉直时与轴的夹角分别为30°和45°,问球的角速度在什么范围 内两绳始终有张力?(g取10 m/s2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241723416713312.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241723416713312.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172341687611.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172341905445.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172342139363.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172341905445.png)
试题分析:当上绳绷紧,下绳恰好伸直但无张力时,小球受力如图
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241723433251574.jpg)
由牛顿第二定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172343543908.png)
又有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172343949605.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172344370767.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172341905445.png)
当下绳绷紧,上绳恰好伸直无张力时,小球受力如图
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241723449941749.jpg)
由牛顿第二定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172345010889.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172345213541.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172341905445.png)
故当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172341687611.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172341905445.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172342139363.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172341905445.png)
点评:本题的两个临界条件是上面绳子绷紧,下面绳子刚好拉直但没有拉力时角速度最小;当下面绳子绷紧,上面绳子刚好拉直但没有拉力时角速度最大。
![](http://thumb2018.1010pic.com/images/loading.gif)
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