The elevator of the television tower accelerates to a speed of 7 m / s in 15 seconds. For the same time it stops.

The elevator of the television tower accelerates to a speed of 7 m / s in 15 seconds. For the same time it stops. How much will the weight of a person change at the beginning and at the end of the lift movement.

V0 = 0 m / s.

V = 7 m / s.

t = 15 s.

g = 9.8 m / s2.

P1 / P -?

P / P2 -?

Where P1 is the weight of a person when accelerating the elevator, P is the weight of a person in a stationary elevator, P2 is the weight of a person when braking the elevator.

Only 2 forces act on a person in the elevator: gravity Ft directed vertically downward, force N of floor pressure on the passenger’s legs directed vertically upward.

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

When the elevator accelerates to the top, its acceleration a will also be directed upward.

For projections onto the vertical axis 2, Newton’s law will take the form: m * a = – Ft + N.

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

a = (V – V0) / t = V / t.

Р1 = m * (g + V / t).

When braking the elevator, its acceleration a will be directed 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 – a).

P2 = m * (g – V / t).

P = m * g.

P1 / P = m * (g + V / t) / m * g = (g + V / t) / g.

P1 / P = (9.8 m / s2 + 7 m / s / 15 s) / (9.8 m / s2) = 1.05.

P / P2 = m * g / m * (g – V / t) = g / (g – V / t).

P / P2 = 9.8 m / s2 / (9.8 m / s2 – 7 m / s / 15 s) = 1.05.

Answer: during acceleration, the weight increased by 5%, while braking, it will decrease by 5%.