The lift accelerates upward with an acceleration of 1 m / s2. With what force does it press

The lift accelerates upward with an acceleration of 1 m / s2. With what force does it press on the floor lying in the elevator weighing 20 kg? Solve the problem under the condition that the elevator brakes with the same acceleration.

a = 1 m / s2.

m = 20 kg.

g = 10 m / s2.

P1 -?

P2 -?

During the movement of the elevator, 2 forces act on the load: the force of gravity Ft, directed vertically downward, the force N, with which the floor of the elevator acts on it, directed vertically upward.

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

1) Elevator acceleration 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).

According to Newton’s 3 law, N = P1.

Р1 = m * (a + g).

Р1 = 20 kg * (1 m / s2 +10 m / s2) = 220 N.

2) The acceleration of the elevator is 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 = m * g – m * a = m * (g – a).

According to Newton’s 3 law, N = P2.

P2 = m * (g – a).

Р1 = 20 kg * (10 m / s2 – 1 m / s2) = 180 N.

Answer: P1 = 220 N, P2 = 180 N.