How fast should the rider move on a convex bridge with a radius of 10 m

How fast should the rider move on a convex bridge with a radius of 10 m so that the rider’s weight in the middle of the bridge is equal to half of the gravity acting on him?

R = 10 m.
g = 9.8 m / s ^ 2.
P = Fт / 2.

V -?

The force of gravity Ft is determined by the formula: Ft = m * g.

Let’s write 2 Newton’s law when moving on the bridge: m * a = m * g – N, where N is the reaction force of the bridge.

N = m * g – m * a.

According to Newton’s 3 laws: the force N, with which the bridge presses on the motorcyclist, is equal to the force P, with which the motorcyclist presses on the bridge.

P = N.
P = m * g – m * a.
m * g / 2 = m * g – m * a.
m * g / 2 = m * a.
g / 2 = a.

Centripetal acceleration a has the formula: a = V ^ 2 / R.

g / 2 = V ^ 2 / R.
V = √ (g * R / 2).
V = √ (9.8 m / s ^ 2 * 10 m / 2) = 7 m / s.

Answer: A motorcyclist must travel across the bridge at a speed of V = 7 m / s.