题目内容
物体A质量为
,用两根轻绳B、C连接到竖直墙上,在物体A上加一恒力F,若图中力F、轻绳AB与水平线夹角均为
,要使两绳都能绷直,求恒力F的大小。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615129289.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615145274.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146151602939.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615176393.gif)
要使两绳都能绷直,必须
,再利用正交分解法作数学讨论。作出A的受力分析如图,由正交分解法的平衡条件:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146152543016.jpg)
①
②
解得
③
④
两绳都绷直,必须![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615191351.gif)
由以上解得F有最大值
,解得F有最小值
,所以F的取值为
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615191351.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146152543016.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615254459.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615269434.gif)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615285395.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615301438.gif)
两绳都绷直,必须
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615191351.gif)
由以上解得F有最大值
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615332338.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615347338.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114615176393.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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