Question

A 65-kg person descends in an elevator that briefly, when leaving a floor, accelerates at 0.20 g.

(a) If that person stands on a scale during this acceleration: what is the force of gravity on the person and what does the scale read?

(b) What does the scale read when the elevator descends at a constant speed of 2.0 m/s?

Answer 1

a) the scale records and displays the normal force acting on it

Newton's second law is

Sum of forces = ma

in this case, the sum of forces are the normal force acting up, and the weight of the person acting down, these combine to produce the acceleration of -0.2g

Therefore, Newton's second law becomes:

Sum of forces = N - mg = ma

N - mg = m(-0.2g) =-0.2mg

N=mg-0.2mg = 0.8mg

the scale will record 80% of her weight (or mass), or 52 kg

b) if the elevator is moving at constant speed, either up or down, there is no acceleration and the scale measure the normal weight