# An elevator with a person moves vertically upward with an acceleration of 0.25 m / s2.

**An elevator with a person moves vertically upward with an acceleration of 0.25 m / s2. If the weight of a person in an elevator is 758.5 N, then the weight of a person is?**

a = 0.25 m / s2.

g = 9.8 m / s2.

P = 758.5 N.

m -?

The weight of the body P is the force with which the body presses on the support or stretches the suspension.

When the body moves with acceleration directed upward, 2 forces act: gravity Ft directed vertically downward, force N, with which a support (lift floor) acts on the body, directed vertically upward.

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

For projections on the vertical axis of the OU, which is directed vertically upward, 2 Newton’s law will take the form: m * a = – Fт + N.

N = Ft + m * a.

The force of gravity Ft is determined by the formula: Ft = m * g.

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

According to Newton’s 3 laws, the force N with which the floor presses on the body is equal to the force with which the body presses on the floor P: N = P.

P = m * (a + g).

m = P / (a + g).

m = 758.5 N / (0.25 m / s2 + 9.8 m / s2) = 72.2 kg.

Answer: a person has a mass m = 72.2 kg.