题目内容
如图所示,光滑的水平面上钉有两枚铁钉A和B,相距0.1 m、长1 m的柔软细绳拴在A上,另一端系一质量为0.5 kg的小球,小球的初始位置在AB连线上A的一侧.把细线拉紧,给小球以2 m/s的垂直细线方向的水平速度使它做圆周运动.由于钉子B的存在,使线慢慢地缠在A、B上. 如果细线的最大拉力
为7 N,从开始运动到细线断裂需经历多长时间?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225458403.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152254744590.png)
8.2S
小球转动时,由于细线逐步绕在a、b两钉上,小球的转动半径会逐渐变小,但小球转动的线速度大小保持不变.
小球交替地绕a、b做匀速圆周运动,因线速度不变,随着转动半径的减小,线中张力![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225520309.png)
不断增大,每转半圈的时间
不断减小.
在第一个半圈内,
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225598589.png)
在第二个半圈内,
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225708809.png)
在第三个半圈内,
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225770865.png)
在第
个半圈内,
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225848979.png)
令
,得
,所以经历的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225957675.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152259883082.png)
小球交替地绕a、b做匀速圆周运动,因线速度不变,随着转动半径的减小,线中张力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225520309.png)
不断增大,每转半圈的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225552271.png)
在第一个半圈内,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225567705.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225598589.png)
在第二个半圈内,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225661911.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225708809.png)
在第三个半圈内,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225754988.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225770865.png)
在第
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225786304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152258321069.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225848979.png)
令
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225864702.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225895427.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115225957675.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152259883082.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目