A car weighing 2000 kg at the top of the convex bridge moves with

A car weighing 2000 kg at the top of the convex bridge moves with an acceleration of 2.5 m / s2. Determine the elastic force acting from the axle on the vehicle.

m = 2000 kg.

g = 9.8 m / s2.

a = 2.5 m / s2.

N -?

When passing the upper point of the convex bridge, 2 forces act on the car: gravity Ft directed vertically downward, the reaction force of the bridge N to the car directed vertically upward.

2 Newton’s law in vector form will have the form: m * a = Fт + N.

Since the centripetal acceleration is always directed to the center of the circle, then, in this case, it will be directed vertically downward.

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).

N = 2000 kg * (9.8 m / s2 – 2.5 m / s2) = 14600 N.

Answer: at the upper point of the trajectory, the elastic force of the bridge N = 14600 N acts on the car.