Question

A lift moves i)up

and ii) down with an
acceleration of 2 ms
{s}^{ - 2} . In cach case, calculate
the reaction of the floor on a man
of mass 50kg standing in the lift.
​

Answer 1

i) The reaction of the floor on the 50 kg man in the lift to lift up the man is 590 Newtons

ii) The reaction of the floor on the 50 kg man in the lift to move down the man is 390 Newtons

Step-by-step explanation:

i) The acceleration of the lift upwards, a = 2 ms⁻²

The mass of the man standing in the lift, m = 50 kg

According to Newton's third law of motion, action and reaction are equal and opposite

Therefore, the force with which the elevator lifts the man = The reaction of the floor on the 50 kg man in the lift to lift up the man = The action of the man on the floor

∴ The force with which the elevator lifts the man up, F = The weight of the man, m·g + The force of the upward motion of the man, m·a

F = m·g + m·a

Where;

g = The acceleration due to gravity = 9.8 m/s²

m = The mass of the man = 50 kg

a = The acceleration of the lift = 2 m/s²

∴ F = 50 kg × 9.8 m/s² + 50 kg × 2 m/s² = 590 Newtons

The reaction of the floor on the 50 kg man in the lift to lift up the man = The force with which the elevator lifts the man up, F = 590 Newtons

ii) The reaction of the floor on the man when the acceleration of the lift is downwards, a = 2 ms⁻², is given as follows;

The force with which the elevator takes the man downwards, F = The reaction of the floor on the 50 kg man in the lift to lift up the man

The force with which the elevator takes the man downwards, F = The weight of the man, m·g - The force of the downward motion of the man, m·a

F = m·g - m·a

∴ F = 50 kg × 9.8 m/s² - 50 kg × 2 m/s² = 390 Newtons

The reaction of the floor on the 50 kg man in the lift to move down the man = The force with which the elevator takes the man downwards, F = 390 Newtons