Scale Reading in Elevator

## Question:

A person weighs a fish on a spring scale attached to the ceiling of an elevator. If the true weight of the fish is 40 N, what would be the spring readings if the elevator moves a) upward with an acceleration of 2 m/s squared. 2) Downward with an acceleration of 2 m/s squared.

Please help;
## Answer:

The apparent weight of the fish is its acceleration times its mass. The mass is the weight divided by the acceleration. When the acceleration is due entirely to gravity the weight is 40 N so the mass is 40 N/9.8 m/s/s = 4.08 kg. The mass is unaffected by any reasonable elevator velocity. The total acceleration of the fish when the elevator is on its way up is the 9.8 due to gravity and the 2 due to the motion of the scales. So the scale reading will be 11.8*4.08 = 48.144 N. On the way down the motion of the scales relieves some of the acceleration due to gravity so the scale reading will be 7.8*4.08 = 31.824 N.