Question

A woman stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.77 of her regular weight.

Calculate the magnitude of the acceleration of the elevator.

Answer 1

As the woman stands on the motionless elevator, the weight of the woman (m = mass of the woman) will acts in downward direction.

Also the normal force N will acts in upward direction.

Now the elevator moves with an acceleration a.

If we consider the upward motion as +ve, the net force acting on the woman is,

When the elevator moves the scale only reads her weight 0.77 of her regular weight.

So

So,

So the magnitude of acceleration of the elevator is  

(-ve sign indicates the elevator is moving in downward direction)