A person stands on a weighing machine placed on the floor of an elevator. The elevator starts moving upwards with a certain acceleration, proceeds with a uniform velocity for a while, and finally decelerates to a stop. The maximum and minimum weights registered are 72 kg and 60 kg . Given that the magnitudes of the acceleration and the deceleration are identical, determine the true weight of the person. Take g = 9.9

Step-by-step solution

Let m be the true mass of the person and a be the magnitude of acceleration and deceleration. When the elevator accelerates upwards, the apparent weight is maximum. The reading on the weighing machine is given by: m_ max = m(g + a) g = m (1 + a g ) = 72 When the elevator decelerates upwards, the apparent weight is minimum. The reading on the weighing machine is given by: m_ min = m(g - a) g = m (1 - a g ) = 60 Adding the two equations, we get: m (1 + a g ) + m (1 - a g ) = 72 + 60 2m = 132 m = 66 kg