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.