An arched bridge is to be designed that cars may pass over safely a a speed of 180km/h without jumping off the road.what should the minimum or maximum value of the radius of curvature of the arch be?
1 Answer
255 m.
Explanation:
If we approximate the bridge to a circular path with radius R, and taking the highest point of the bridge's curvature as the point of reference for the v = 180 km/h speed, then the centripetal force (Fc) in this case may be written as:
Also, since
However, in a limit situation where the car would lose contact with the bridge, we would have N = 0, which means that the centripetal force would be equal to the car's weight. In this case, then:
Therefore:
Taking