The weight of a body in an elevator moving with an acceleration directed upwards and equal to 5 m / s

The weight of a body in an elevator moving with an acceleration directed upwards and equal to 5 m / s turned out to be equal to 100N What is the mass of this body?

a = 5 m / s2.

P = 100 N.

g = 10 m / s2.

m -?

Two forces act on the bodies in the elevator: the force of gravity Ft directed vertically downward, and the force N of the pressure of the floor of the elevator on the body directed vertically upward.

2 Newton’s law will have the form: m * a = Fт + N.

Since the elevator moves with acceleration a directed upwards, the body in the elevator has the same acceleration.

For projections onto a vertical axis directed vertically upward, 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 acts on the body is equal to the force P with which the body presses on the floor, that is, the weight of this body P: N = P.

P = m * (a + g).

m = P / (a ​​+ g).

m = 100 N / (5 m / s2 + 10 m / s2) = 6.6 kg.

Answer: the body has a mass m = 6.6 kg.