A weighing machine installed in a lift. What will happen to the machine reading if lift starts accelerating downward?

Question

John is standing on a weighing machine installed in a lift. The weighing machine shows the reading 50 kg when the lift is at rest.

What will happen to the reading of the machine if the lift starts accelerating downward?

Answer 1

The weighing machine converts force (Newton) exerted by the man into a number that is mass (kg) assuming acceleration due to gravity = (g) = 9.81 (m/s^2).
At rest the weighing machine experiences 50 × 9.81 = 490.5 N
This is then divided by 9.81 to get 50kg
When the lift accelerates downward with an acceleration 'a' the floor of the lift will not be able to give an equal and opposite reaction to the weight of the man. This reaction is what the scale relies on to get the reading, which is true when the ground and the person is stationary. Therefore the new weight in terms of force = 50 × (9.81 - a) N
so the weighing machine will indicate 50 × (9.81 - a)/9.81 kg as the new weight which is less than 50 kg or = 0 kg when a = 9.81 = g (When the lift is free falling).