题目内容
(10分)如图所示,用不可伸长的轻绳AC和BC吊起一质量不计的沙袋,绳AC和BC与天花板的夹角分别为60°和30°。现缓慢往沙袋中注入沙子。重力加速度g取10m/s2。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030113173913.jpg)
(1)当注入沙袋中沙子的质量m=10kg时,求绳AC和BC上的拉力大小FAC和FBC。
(2)若AC能承受的最大拉力为150N,BC能承受的最大拉力为100N,为使绳子不断
裂,求注入沙袋中沙子质量的最大值M。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030113173913.jpg)
(1)当注入沙袋中沙子的质量m=10kg时,求绳AC和BC上的拉力大小FAC和FBC。
(2)若AC能承受的最大拉力为150N,BC能承受的最大拉力为100N,为使绳子不断
裂,求注入沙袋中沙子质量的最大值M。
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011364661.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011332728.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011348634.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011364661.png)
试题分析:装置受力图如右图所示
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030114104559.jpg)
(1)沙桶处于静止,根据二力平衡有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011426520.png)
受力分析如图,AC和BC两端绳子拉力分别沿各自绳子的方向,二力的合力与T等大反向,做二力合成的平行四边形如图
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030114421038.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011473948.png)
(2)AC和BC两段绳子方向不变,要保持平衡,二力的拉力方向不变,二力合成的平行四边形仍然如上图
所以有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011488778.png)
而
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011504788.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011535741.png)
所以AC更容易被拉断 (2分)
此时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030115511165.png)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003011566872.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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