How fast a car must travel on a convex bridge with a radius of 30 m to get off the road surface

How fast a car must travel on a convex bridge with a radius of 30 m to get off the road surface. Vehicle weight 2t.

Given:

R = 30 meters – radius of the convex bridge;

m = 30 tons = 30,000 kilograms – vehicle weight;

g = 10 Newton / kilogram – acceleration of gravity.

It is required to determine v (meter per second) – how fast the car must move to break away from the convex bridge.

In order for the car to be able to break away from the convex bridge, the following inequality must be true:

F gravity <F centrifugal;

m * g <m * a;

g <a;

g <v ^ 2 / r;

g * r <v ^ 2;

v> (g * r) ^ 0.5;

v> (10 * 30) ^ 0.5;

v> 300 ^ 0.5;

v> 17.3 m / s.

Answer: The car must move at a speed greater than 17.3 m / s.