Question

Apparent Weight You take a ride in a fast
elevator to the top of a tall building and ride
back down. Compare your apparent and real
weights at each part of the journey. Sketch
free-body diagrams to support your answers.

Answer 1

Consider two cases , where the fast elevator is going up and going down.

For each of the cases, apparent weight is given by R as shown in the free body diagram.

For the going upward case,

From the Free body diagram.

$F=ma\\ R_1 -mg= ma \\ R_1=m(g+a)$

Therefore the apparent weight will be greater than the real weight if the elevator is going upwards and accelerating $(a>0)$ and will be lower than the real weight if the elevator is decelerating (a<0).

For the going downward case,

From the Free body diagram.

$F=ma\\ mg-R_2=ma\\ R_2=m(g-a)\\$

Therefore the apparent weight will be lower than the real weight if the elevator is going downwards and accelerating $(a>0)$ and will be higher than the real weight if the elevator is decelerating $(a<0)$ .