题目内容
在各种公路上拱形桥是常见的,质量为m的汽车在拱形桥上以速度v前进,桥面的圆弧半径为R,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241329111802099.jpg)
(1)汽车通过桥的最高点时对桥面的压力。
(2)若R取160 m,试讨论汽车过桥最高点的安全速度。(g取10 m/s2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241329111802099.jpg)
(1)汽车通过桥的最高点时对桥面的压力。
(2)若R取160 m,试讨论汽车过桥最高点的安全速度。(g取10 m/s2)
(1)
(2)
40 m/s
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911211690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911242304.png)
(1)汽车通过桥的最高点时受力如图,根据牛顿第二定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911273844.png)
桥面对汽车的支持力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911305838.png)
根据牛顿第三定律,汽车对桥面的压力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911367462.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911211690.png)
(2)若
,汽车对桥面无压力,汽车将腾空从而失控制。所以为安全起见应
,即![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911242304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911570419.png)
代入数据得
40 m/s
汽车过桥时的安全速度应小于144 km/h
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911273844.png)
桥面对汽车的支持力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911305838.png)
根据牛顿第三定律,汽车对桥面的压力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911367462.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911211690.png)
(2)若
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911461472.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911507486.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911242304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911570419.png)
代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132911242304.png)
汽车过桥时的安全速度应小于144 km/h
![](http://thumb2018.1010pic.com/images/loading.gif)
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