Question

What is the weight of a man in a lift when it is moving upwards with acceleration a ?

Answer 1

When the lift moves down with acceleration. he weight measured can be defined as the force which the body applies in the downward direction. Or, mathematically, it can be written as

F = m.a; where a is directed towards the centre of Earth (downwards).

Now, for a body at rest, the acceleration is the gravitational acceleration ‘g’. However, an accelerated body will have some relative acceleration. Considering the downward direction to be positive, we have,

Acceleration due to gravity = g

Downward acceleration inside the lift = a

Therefore, effective acceleration = (g - a)

Total Force in downward direction is given by

F = m.(Effective Acceleration) = m(g - a)

Or, F = mg - ma

Now, since m is always positive and a is positive in downward direction, for a lift moving downwards, we have

mg - ma < mg

Which means, the apparent weight in a lift moving downwards is always less than the actual weight observed at rest.

Note that it is only applicable when the lift is accelerating downwards. Once the lift attains a constant speed, the apparent weight becomes equal to the actual weight when measured for stationary case.

R = m(g-a),

So,the person feels lighter.