题目内容
(18分)如图,质量m=20kg的物块(可视为质点),以初速度v0=10m/s滑上静止在光滑轨道的质量M=30kg、高h=0.8m的小车的左端,当车向右运动了距离d时(即A处)双方达到共速。现在A处固定一高h=0.8m、宽度不计的障碍物,当车撞到障碍物时被粘住不动,而货物继续在车上滑动,到A处时即做平抛运动,恰好与倾角为53°的光滑斜面相切而沿斜面向下滑动,已知货物与车间的动摩擦因数μ=0.5。
(g=10m/s2,sin53°=0.8,cos53°=0.6)求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019308585890.jpg)
(1)车与货物共同速度的大小v1;
(2)货物平抛时的水平速度v2;
(3)车的长度L与距离d.
(g=10m/s2,sin53°=0.8,cos53°=0.6)求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019308585890.jpg)
(1)车与货物共同速度的大小v1;
(2)货物平抛时的水平速度v2;
(3)车的长度L与距离d.
(1)
(2)
(3)
,![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930951590.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930889639.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930904661.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930920552.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930951590.png)
试题分析:(1)车与货物已经到达共同速度,根据动量守恒定律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930967848.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930889639.png)
(2)货物从小车上滑出之后,做平抛运动,根据平抛运动规律可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001931014650.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001931029478.png)
在竖直方向上:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001931045762.png)
在斜面顶点分解速度如图,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001931076789.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019310927127.jpg)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930904661.png)
(3) 对于车,由动能定理,得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019311231065.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930951590.png)
对于货物,全程由动能定理,得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019311541178.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001930920552.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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