A cyclist weighing 60 kg drives through the middle of the convex bridge at a speed of 10 m / s. The radius of curvature is 20 m

A cyclist weighing 60 kg drives through the middle of the convex bridge at a speed of 10 m / s. The radius of curvature is 20 m, g = 10 m / s. The force of the cyclist’s pressure on the bridge is …

m = 60 kg.
g = 10 m / s2.
R = 20 m.
V = 10 m / s.
R – ?
Two forces act on the cyclist when passing the middle of the convex bridge: gravity Ft directed vertically downward, and the reaction force N of the bridge directed vertically upward.
m * a = F + N – 2 Newton’s law in vector form.
For projections onto the vertical axis 2, Newton’s law will take the form: – m * a = – Fт + N.
N = Fт – m * a.
The force of gravity Ft is determined by the formula: Ft = m * g.
N = m * g – m * a = m * (g – a).
The centripetal acceleration a is expressed by the formula: a = V ^ 2 / R.
N = m * (g – V ^ 2 / R).
According to Newton’s 3 Laws, the force N with which the bridge presses on the cyclist is equal to the force P with which the cyclist presses on the bridge: N = P.
P = m * (g – V ^ 2 / R).
P = 60 kg * (10 m / s2 – (10 m / s) ^ 2/20 m) = 300 N.
Answer: when passing the position of the middle of the convex bridge, the cyclist acts on the bridge with a force of P = 300 N.