A car weighing 1500 kg moves along a concave bridge with a radius of 75 m at a speed of 15 m / s.

A car weighing 1500 kg moves along a concave bridge with a radius of 75 m at a speed of 15 m / s. Determine the weight of the vehicle at the lowest point of the bridge.

m = 1500 kg.

g = 10 m / s2.

R = 75 m.

V = 15 m / s.

P -?

The weight of the car P is the force with which the car pushes against the bridge.

Two forces act on the car when passing the lower point of the bridge: gravity Ft directed vertically downward, force N of the bridge pressure on the car directed vertically upward.

m * a = m * g + N – 2 Newton’s law in vector form.

Since the bridge is concave, the centripetal acceleration a will be directed vertically upwards.

For projections onto the vertical axis 2, Newton’s law will take the form: m * a = – Fт + N.

N = m * a + Fт.

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

N = m * a + m * g = m * (a + g).

The centripetal acceleration a is expressed by the formula: a = V2 / R.

N = m * (V ^ 2 / R + g).

According to Newton’s 3 laws, the force N with which the bridge presses on the car is equal in magnitude and oppositely directed, the force with which the car presses on the bridge P: N = – P.

P = m * (V ^ 2 / R + g).

P = 1500 kg * ((15 m / s) ^ 2/75 m + 10 m / s2) = 19500 N.

Answer: the weight of the car at the lowest point of the concave bridge is P = 19500 N.