题目内容
如图14所示,小球的质量为2kg,两根轻绳AB和AC的一端连接于竖直墙上,另一端系于小球上,AC绳水平。在小球上另施加一个方向与水平线成θ=60º角的拉力F,若要使绳子都能伸直,求拉力F的大小范围。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144285501491.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144285501491.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428581318.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428596320.gif)
小球受力如图所示,由力的平衡条件得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144286121584.gif)
Fcosθ=F1cosθ+F2
Fsinθ+F1sinθ=mg
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428659547.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428674689.gif)
要使两绳伸直,则应满足F1≥0;F2≥0;
当F1≥0时,F≤
N
当F2≥0时,F≥=N
故:
N≤F≤
N
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144286121584.gif)
Fcosθ=F1cosθ+F2
Fsinθ+F1sinθ=mg
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428659547.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428674689.gif)
要使两绳伸直,则应满足F1≥0;F2≥0;
当F1≥0时,F≤
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428690615.gif)
当F2≥0时,F≥=N
故:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428581318.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428596320.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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