题目内容
两块质量分别为m1、m2的木板,被一根劲度系数为k轻弹簧连在一起,并在m1板上加压力F,如图所示,撤去F后,m1板将做简谐运动。为了使得撤去F后,m1跳起时恰好能带起m2板,则所加压力F的最小值为?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082414040712210626.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082414040712210626.png)
F=(
1g+
2g)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
解:撤去外力
后,
1将在回复力的作用下做简谐振动,依题意当
1运动到最上端时,
2对接触面恰好无压力,故此时回复力为大小为
(
1g+
2g) 3分
由对称性可知,当
1在最下端时,回复力大小也为
(
1g+
2g) 3分
故所施外力大小为 F=(
1g+
2g) 2分
本题考查的是简谐运动的问题。关键是对此简谐运动进行受力分析。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407371174.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407543173.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
由对称性可知,当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407543173.png)
(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
故所施外力大小为 F=(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140407200264.png)
本题考查的是简谐运动的问题。关键是对此简谐运动进行受力分析。
![](http://thumb2018.1010pic.com/images/loading.gif)
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