There is a person weighing 70 kg in the elevator. In which direction and how the elevator moves

There is a person weighing 70 kg in the elevator. In which direction and how the elevator moves, if the weight of a person is 500H.

P = 500 N.

m = 70 kg.

g = 10 m / s2.

a – ?

A person in a moving elevator is affected by 2 forces: gravity Ft directed vertically downward, force N of the elevator floor pressure directed vertically upward.

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

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

According to Newton’s 3 laws, the force N with which the floor of the elevator presses on a person’s legs is equal to the force with which a person presses on the floor of the elevator P: N = P.

P = m * (a + g).

In order for the weight of a person during the movement of the elevator to be less than the force of gravity, the acceleration of the elevator a must be directed vertically downward.

P = m * (g – a).

a = (m * g – P) / m.

a = (70 kg * 10 m / s2 – 500 N) / 70 kg = 2.85 m / s2.

Answer: the acceleration of the elevator a = 2.85 m / s2 should be directed vertically downward. When moving up, the elevator must slow down, when moving down, the elevator must accelerate.