题目内容
一劲度系数k = 800N/m的轻质弹簧两端分别连接着质量均为12kg的物体A、B,将他们竖直静止在水平面上,如图16所示,现将一竖直向上的变力F作用A上,使A开始向上做匀加速运动,经0.4s物体B刚要离开地面,求:(设整个过程弹簧都在弹性限度内,取g = 10m/s2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241302186674036.png)
小题1:此过程中所加外力F的最大值和最小值;
小题2:此过程中力F所做的功。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241302186674036.png)
小题1:此过程中所加外力F的最大值和最小值;
小题2:此过程中力F所做的功。
小题1:t = 0时,外力F最小,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218699849.png)
t = 0.4s时,外力F最大,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241302187301204.png)
小题2:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218777700.png)
(1)t = 0时,弹簧的压缩量为x1
则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218933868.png)
t = 0.4s时,弹簧的伸长量为x2
则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218979890.png)
匀加速运动过程,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218995734.png)
解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130219057720.png)
t = 0时,外力F最小,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218699849.png)
t = 0.4s时,外力F最大,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241302187301204.png)
(2)过程末了时刻A的速度
在A上升的过程中,弹簧由压缩0.15m的状态变为伸长0.15m,弹力所作功的代数和为零,由动能定理有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241302192131194.png)
解得力F所做的功![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218777700.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218870584.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218933868.png)
t = 0.4s时,弹簧的伸长量为x2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218964602.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218979890.png)
匀加速运动过程,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218995734.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130219057720.png)
t = 0时,外力F最小,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218699849.png)
t = 0.4s时,外力F最大,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241302187301204.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130219182973.png)
在A上升的过程中,弹簧由压缩0.15m的状态变为伸长0.15m,弹力所作功的代数和为零,由动能定理有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241302192131194.png)
解得力F所做的功
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130218777700.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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