Motion of a man in a lift

Case (1): When the lift is accelerated upward:

Suppose, ‘R’ be the upward thrust of the floor on the man (normal reaction) and ‘mg’ is the weight of the man acting downwards.

Hence, Unbalanced force = mass × acceleration

            Or, R = mg + ma

            Or, R = m (g + a)

Thus, if the man is standing on weighing machine, it will show a larger weight than ‘mg’.

Case (2): When the lift is accelerate downwards:

            R+F = mg

           Or, R = mg – ma = m (g – a)

Case (3): When the lift moves with uniform velocity (or is at rest):

In this case, a = 0    So, R = mg.

In the case of free fall of the lift, a = g,

                                    Then, r = m (g – a), i.e. the man will feel weightlessness.