题目内容
当汽车通过桥面粗糙的拱形桥顶点的速度为10m/s时,车对桥顶的压力为车重的
,如果要使汽车行驶至该桥顶时不受摩擦力作用,则汽车通过桥顶的速度应为( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714445339.png)
A.25m/s | B.20m/s | C.15m/s | D.30m/s[ |
B
分析:车做圆周运动,车对桥的压力为重力的
时,由重力和支持力的合力提供向心力可求出桥的半径,车对桥无压力时,重力恰好提供向心力,可由向心力公式列式求出车速.
解答:解:车对桥顶的压力为车重的
时
mg-
mg=m![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714648400.png)
解得
R=
=
=40m
车在桥顶对桥面没有压力时
mg=m![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714897418.png)
解得
v1=
=
=20m/s
故选B.
点评:本题关键找出向心力来源后根据向心力公式和牛顿第二定律联立列式求解!
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714445339.png)
解答:解:车对桥顶的压力为车重的
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714445339.png)
mg-
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714445339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714648400.png)
解得
R=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714741434.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714772485.png)
车在桥顶对桥面没有压力时
mg=m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714897418.png)
解得
v1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714944421.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132714975499.png)
故选B.
点评:本题关键找出向心力来源后根据向心力公式和牛顿第二定律联立列式求解!
![](http://thumb2018.1010pic.com/images/loading.gif)
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