A skier weighing 50 kg moves at a speed of 36 km / h along the concave and then along the convex

A skier weighing 50 kg moves at a speed of 36 km / h along the concave and then along the convex sections of the road with a radius of curvature of 20 m. Determine the weight of the skier in the middle of the bulge.

m = 50 kg.

g = 10 m / s2.

V = 36 km / h = 10 m / s.

R = 20 m.

P -?

The weight of the skier P is the force with which he acts on the bridge when moving. Since the bridge is in the shape of a circle, the skier moves with centripetal acceleration, which is directed towards the center of the circle.

On the convex section of the bridge, the centripetal acceleration is directed vertically downward, as well as the force of gravity.

2 Newton’s law will have the form: – m * a = N – m * g.

N = m * g + m * a = m * (g – a).

The centripetal acceleration of the skier a is expressed by the formula: a = V ^ 2 / R.

N = m * (g – V ^ 2 / R).

According to Newton’s 3 law, the action force N is equal to the reaction force P: N = P.

P = m * (g – V ^ 2 / R).

P = 50 kg * (10 m / s2 – (10 m / s) ^ 2/20 m) = 250 N.

Answer: in the middle of the convex bridge, the skier’s weight is P = 250 N.