题目内容
(17分)如图所示,质量 m=2 kg 的小球以初速度 v0沿光滑的水平面飞出后,恰好无碰撞地进入光滑的圆弧轨道,其中圆弧 AB 对应的圆心角θ=53°,圆半径 R=0.5 m.若小球离开桌面运动到 A 点所用时间t=0.4 s . (sin53°=0.8,cos53°=0.6,g=10 m/s2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017449184380.jpg)
(1)求小球沿水平面飞出的初速度 v0的大小?
(2)到达 B 点时,求小球此时对圆弧的压力大小?
(3)小球是否能从最高点 C 飞出圆弧轨道,并说明原因.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017449184380.jpg)
(1)求小球沿水平面飞出的初速度 v0的大小?
(2)到达 B 点时,求小球此时对圆弧的压力大小?
(3)小球是否能从最高点 C 飞出圆弧轨道,并说明原因.
(1)3m/s (2)136N (3) 能
试题分析:(1)小球离开桌面后做平抛运动
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001744965376.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001744980501.png)
根据几何关系可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001744996697.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001745011614.png)
(2)小球到达A点时的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001745027940.png)
从A到B过程中满足机械能守恒,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017450431322.png)
到达B点时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001745058877.png)
整理得:N=136N
(3)小球从B到C点过程中满足机械能守恒,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017450741103.png)
而
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001745089703.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001745121781.png)
因此小球不脱离轨道,能从C点飞出
![](http://thumb2018.1010pic.com/images/loading.gif)
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