A passenger car weighing 1000 kg travels at a speed of 28.8 km / h on a convex bridge with a radius of 40 m.

A passenger car weighing 1000 kg travels at a speed of 28.8 km / h on a convex bridge with a radius of 40 m. Determine the force of pressure on the middle of the bridge. Can we assume that this force is equal to the weight of the car?

m = 1000 kg.

g = 9.8 m / s2.

V = 28.8 km / h = 8 m / s.

R = 40 m.

P -?

The force P with which the car acts on the axle is called the weight of the car.

Let’s write 2 Newton’s law in vector form: m * a = m * g + N, where m is the mass of the car, a is the centripetal acceleration of the car, m * g is the gravity of the car, N is the force with which the bridge acts on the car.

In projections, on the vertical axis directed upward, 2 Newton’s law will have the form: – m * a = – m * g + N.

N = m * g – m * a = m * (g – a).

Centripetal acceleration a is determined by the formula: a = V2 / R.

N = m * (g – V ^ 2 / R).

According to Newton’s 3 laws, N = R.

P = m * (g – V ^ 2 / R).

P = 1000 kg * (9.8 m / s2 – (8 m) ^ 2/40 m) = 8200 N.

The weight of the car when driving on a horizontal road is Pg = m * g.

Pr = 1000 kg * 9.8 m / s2 = 9800 N.

Answer: in the middle of the bridge, the car acts with a force of P = 8200 N.