The cyclist moves along a convex bridge with a radius of curvature of 40m.

The cyclist moves along a convex bridge with a radius of curvature of 40m. How fast the cyclist needs to be in order for him to slip through the hole in the middle of the bridge.

g = 10 m / s2.

R = 40 m.

V -?

In order for the cyclist to be able to slip through the hole in the middle of the convex bridge, at the time of passage he must be in a state of weightlessness. That is, its weight P must be equal to 0.

m * a = m * g – N.

a = V ^ 2 / R

m * V ^ 2 / R = m * g – N.

According to Newton’s 3 law: N = R.

m * V ^ 2 / R = m * g.

V ^ 2 / R = g.

V ^ 2 = g * R.

V = √ (g * R).

V = √ (10 m / s2 * 40 m). = 20 m / s.

Answer: in order to slip through the hole in the middle of the convex bridge, the cyclist must ride at a speed of V = 20 m / s.