题目内容
如图所示,半径
=1.25m的l/4光滑圆弧轨道
竖直固定,其末端
切线水平,并与水平传送带相连,已知小滑块的质量为
=0.5kg,滑块与传送带间的动摩擦因数
=0.1,传送带
长度为
=1.5m,
、
两轮半径
=0.4m,当传送带静止时,用
="4" N的水平拉力将滑块从
端由静止开始向左拉动。
取10m/s2。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241952500196339.png)
(1)若滑块到达
端时撤去拉力
,求:滑块沿弧形槽上升的最大高度;
(2)问题(1)中的滑块,从高点沿弧形槽再滑回
端时,轨道对滑块的支持力多大?
(3)若拉力
作用一段距离后撤去,滑块到达光滑曲面某一高度而下滑时,以
、
两轮以角速度
=15rad/s顺时针转动,为使滑块能在
轮最高点
离开传送带飞出,则拉力
作用的最短距离需多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195238646303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195239723396.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195240425309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195241220337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195242125301.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195242687398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195243607258.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195244496283.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195245432299.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195246524260.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195247289302.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195248225313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195249208273.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241952500196339.png)
(1)若滑块到达
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195240425309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195247289302.png)
(2)问题(1)中的滑块,从高点沿弧形槽再滑回
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195240425309.png)
(3)若拉力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195247289302.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195244496283.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195245432299.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195256087308.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195245432299.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195248225313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195247289302.png)
(1)h=1.05m(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195259472561.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195258848693.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195259472561.png)
试题分析:(1)根据动能定理有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195300330952.png)
即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195300908829.png)
(2)从高点滑回B点过程中,根据机械能守恒定律有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195301781830.png)
在B点有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195302343926.png)
解以上两式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241953029511206.png)
(3)根据题意,滑块要从b轮最高点C离开传送带飞出,则滑块运动至C点的速度最小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195303419716.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241953044961079.png)
由于传送带的速度v带=rω=6m/s,滑块在B点的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195305135771.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195306149451.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241953066801106.png)
为了使滑块运动到C点时速度大于2m/s,则B点的速度最小为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195307148769.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195307865650.png)
设拉力F作用的最短距离为x,则根据动能定理
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241953087541058.png)
代入数据可以求得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824195259472561.png)
点评:本题主要考察了动能定理及运动学基本公式的应用,要求同学们能正确分析物体的运动情况.
![](http://thumb2018.1010pic.com/images/loading.gif)
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