Bathroom Scale: Motion

Question

A 750-Newton man is standing on a bathroom scale in an elevator. When the elevator is moving, the man notices that the scale is reading 780 N. How would you describe the motion of the elevator?

 

Answer 1

The elevator must be accelerating upward, which increase the normal force that the scale exerts on his body.  If he was not accelerating up, the normal force of the scale would just equal 750 N.

 

In this problem, the balance of forces is:

 

W' = W + ma,

 

where W' is the measured weight during acceleration, W = mg is his "rest" weight, and a = acceleration

 

m = W/g

 

W' = W + (W/g)*a

 

a = (W' - W) * (g/W) = (780-750)*(9.8/750) m/s^2 = 0.392 m/s^2

 

So the elevator is accelerating up at a rate of 0.392 m/s^2. 

Answer 2

The elevator must be ascending because now the floor of the elevator is pushing against the scale with a force of 30N. The scale in turn pushes against the 750N man, causing the reading to increase by 30N.