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`.

Explanation

a. the tension i the string is found out for the different conditions from the free diagram as shown below

`T-(W+0.05xx1.2`
` =0.05(9.8+1.2)`
`= 0.55N`
b. Now
`T+0.05xx1.2-0.05xx9.8=0`
` rarr T=0.05xx9.8=0.05xx1.2`
`= 0.05(9.8-1.2)`
`=0.05xx8.6`
`=0.43N`
c. When the elevator makes uniform motion,
`T-W=0`
`rarr T=W=0.05xx9.8=0.49N`
d. `T+ 0.05xx1.2-w=0`
`rarr T=w-0.05xx1.2`
`=0.05(9.8-1.2)=0.43N`
e.`T-(W+0.05xx1.2)=0`
`rarr T= W+0.05xx1.2`
` rarr 0.05(9.8+1.2)=0.55N`.
f. When the elevator goes down with uniform velocity acceleration =0.
`:. T-W=0`
`rarr T=W= 0.05xx9.8`
`=0.49N`.