A man weighing 60 kg presses the mass on the elevator with a force of 480 N. What is the acceleration of the elevator?

m = 60 kg.

g = 10 m / s2.

P = 480 N.

а – ?

A person in the elevator is under the influence of 2 forces: gravity Ft directed vertically downward, and the force of pressure of the floor of the elevator on the legs N directed vertically upward.

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

According to Newton’s 3 law, the force of action is equal to the force of reaction.

Therefore, the force N with which the floor presses on the legs is equal in magnitude and opposite to the directional force with which the legs press on the floor, that is, the weight P: P = N.

m * a = Ft + P.

a = (Ft + P) / m.

For projections onto a vertical axis directed vertically upward, 2 Newton’s law will take the form: a = (- Ft + P) / m = (P – m * g) / m.

a = (480 N – 60 kg * 10 m / s2) / 60 kg = – 2 m / s2.

The “-” sign indicates that the acceleration of the lift should be directed vertically downward.

Answer: the acceleration of the elevator is directed vertically downwards and is numerically a = 2 m / s2.