Question

A man of mass 80 kg is travelling in a lift which is moving upwards. If the lift
comes to rest from a velocity of 2 m/s in a 2 seconds, find the force exerted by the
man on the lift floor if the deceleration is constant. What would be the reaction if the
lift were travelling downwards?

Answer 1

Question # 79719

A man of mass $80\,\mathrm{kg}$ is travelling in a lift which is moving upwards. If the lift comes to rest from a velocity of $2\,\mathrm{m/s}$ in a 2 seconds, find the force exerted by the man on the lift floor if the deceleration is constant. What would be the reaction if the lift were travelling downwards?

Answer:

According to Newton’s Second Law the force $F$ exerted by the man on the lift floor is given by

$$F = m(g - a),$$

where $m = 80\,\mathrm{kg}$ – the mass of the man,

$g = 9.81\,\mathrm{m/s^2}$ – the acceleration due to gravity,

$a$ – the constant upward deceleration of the man, which is given by

$$a = \frac{\Delta u}{t},$$

where $\Delta u = 2\,\mathrm{m/s}$ – the change in the velocity of the man,

$t = 2\,\mathrm{s}$ – the time of change of the velocity.

Substitute into (2) and (1):

$$a = \frac{2}{2} = 1\,\mathrm{m/s^2},$$ $$F = 80 \cdot (9.81 - 1) = 704.8\,\mathrm{N}.$$

In case of lift travelling downward, the direction of the deceleration changes resulting in transformation of (1) to form

$$F = m(g + a),$$

Substitute into (3) to obtain the force exerted by the man on the lift floor when lift moves downward

$$F = 80 \cdot (9.81 + 1) = 864.8\,\mathrm{N}.$$