Q. 154.5( 8 Votes )

# A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while and finally decelerates to stop. The maximum and the minimum weights recorded are 72 kg and 60 kg. Assuming that the magnitudes of the acceleration and the deceleration are the same, find (a) the true weight of the person and (b) the magnitude of the acceleration. Take g = 9.9 m/s^{2}.

Answer :

Let actual weight of the person be

Given:

Maximum weight

Minimum weight

When the elevator moves with acceleration , a pseudo force acts on the person in the downward direction.

In this case the weight is maximum as measured by the weighing machine, -----(1)

Where is the acceleration of the elevator.

When the elevator moves with deceleration , a pseudo force acts on the person in the upward direction.

In this case the weight is minimum as measured by the weighing machine, -----(2)

Adding (1) and (2) we get,

Thus, the weight

Subtracting (2) from (1)

Thus, the magnitude of acceleration,

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