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
Carlos S.
Jan 17, 2018

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:

F_c = W - N, where 'W' and 'N' denote the car's weight and normal forces, respectively.

Also, since F_c = mv^2/R, with m being the car's mass; then we can write that

W - N = mv^2/R.

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:

mg = mv^2/R.

Therefore:
R = v^2/g.

Taking g = 9,81 m/s^2 and the speed in m/s:

R = 50^2/9.81

R = 255 m, approximately.

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