Question

A 45.0-kg person steps on a scale in an elevator. The scale reads 460 n. What is the magnitude of the acceleration of the elevator?

Answer 1

`0.42 m/s^2`

Step-by-step explanation:

There are two forces acting on the person as he's standing on the scale in the elevator:

- Its weight,
`mg`, downward, with m = 45.0 kg being his mass and g = 9.8 m/s^2 being the acceleration of gravity

- The normal reaction exerted by the scale on the person, N, upward, which is equal to the value read on the scale, N = 460 N

Using Newton's second law, we can write

`N-mg = ma`

Where a is the acceleration of the person (and of the elevator). Solving for a,

`a=(N-mg)/(m)=(460-(45)(9.8))/(45)=0.42 m/s^2`

And since we chose positive as the upward direction, the acceleration is upward.