# With what acceleration should the elevator move so that the body lying on its floor has triple weight?

P1 = 3 * P.

g = 9.8 m / s ^ 2.

a – ?

Body weight P is the force with which the body presses on the support or stretches the suspension. At rest, the weight of the body P is determined by the formula: P = m * g, where m is the mass of the body, g is the acceleration of gravity.

Р1 = 3 * m * g.

When the acceleration of the elevator is directed upwards, 2 forces act on the body that is in it: the gravity force m * g, directed vertically downward, and the reaction force of the floor of the elevator N, directed vertically upward.

Let’s write 2 Newton’s law: m * a = N – m * g.

N = m * a + m * g = m * (a + g).

According to Newton’s 3 laws: P1 = N.

3 * m * g = m * (a + g).

3 * g = a + g.

a = 2 * g.

a = 2 * 9.8 m / s ^ 2 = 19.6 m / s ^ 2.

Answer: the lift must move with an acceleration a = 19.6 m / s ^ 2, which is directed vertically upwards.