## Apparent weight of a man in a lift

### Apparent weight of a man in a lift

When a person of man m is standing on a weighting machine placed in lift, the actual weight of a person = mg. This acts on the weighting machine which offers a reaction R, given by the reading of weighing machine. This reaction exerted by the surface of contact on the man is the apparent weight of the man. The apparent weight is different in different situation.
1) When elevator is at rest or moving with a uniform velocity (upwards or downwards) the apparent weight, R = mg i.e., actual weight of a man.
2) When elevator is accelerating downwards with acceleration a, then mg-R= ma or R= m (g-a). Thus the apparent weight of the man becomes less than the actual weight, when elevator is accelerating downwards.
If a= g, then R = m (g-g) =0.
It means apparent weight of a man in an elevator falling down freely with acceleration equal to acceleration due to gravity is zero.
3) When elevator is accelerating upwards with acceleration a, then R-mg = ma or R = m (g + a) Thus, the apparent weight of the man becomes more than the actual weight, when the elevator is accelerating upwards.