题目内容
如图15所示,质量为m的物体被劲度系数为k2的弹簧2悬挂在天花板上,下面还拴着劲度系数为k1的轻弹簧1,托住下弹簧的端点A用力向上压,当弹簧2的弹力大小为
时,弹簧1的下端点A上移的高度是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144287841024.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428768399.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241144287841024.gif)
弹簧1的下端点A上移的高度是
或![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428815599.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428799576.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428815599.gif)
A点上升的高度等于弹簧2和1缩短的长度之和。
(1)A点上升,使弹簧2仍处于伸长状态时,弹簧2的弹力减小了
,弹簧2比原来缩短⊿x2,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428846494.gif)
弹簧1的弹力为
,压缩量为⊿x1,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428955494.gif)
所以,端点A上移的高度是:
⊿x=⊿x1+⊿x2=
。
(2)A点上升,使弹簧2处于压缩状态时,向下的弹力为
,压缩量为⊿x2',有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114429002503.gif)
所以弹簧2的长度总的缩短量为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114429018924.gif)
弹簧1上的弹力为mg+
=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114429049403.gif)
所以弹簧1的长度的缩短量为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114429064526.gif)
所以,端点A上移的高度是:
⊿x=⊿x1+⊿x2=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428815599.gif)
所以弹簧1的下端点A上移的高度是
或
。
(1)A点上升,使弹簧2仍处于伸长状态时,弹簧2的弹力减小了
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428768399.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428846494.gif)
弹簧1的弹力为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428768399.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428955494.gif)
所以,端点A上移的高度是:
⊿x=⊿x1+⊿x2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428799576.gif)
(2)A点上升,使弹簧2处于压缩状态时,向下的弹力为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428768399.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114429002503.gif)
所以弹簧2的长度总的缩短量为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114429018924.gif)
弹簧1上的弹力为mg+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428768399.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114429049403.gif)
所以弹簧1的长度的缩短量为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114429064526.gif)
所以,端点A上移的高度是:
⊿x=⊿x1+⊿x2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428815599.gif)
所以弹簧1的下端点A上移的高度是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428799576.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114428815599.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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