You've always wondered about the acceleration of the elevators in the 101 story-tall Empire State Building. One day, while visiting New York, you take your bathroom scale into the elevator and stand on them. The scales read 160 lb as the door closes. The reading varies between 130 lb and 180 lb as the elevator travels 101 floors. a. What is the magnitude of the acceleration as the elevator starts upward?
b. What is the magnitude of the acceleration as the elevator brakes to a stop?

a)  a = 4 ft / s² , b) a = -6 ft / s²

Explanation:

The balance is subjected to two forces: the weight of the person directed downward and the spring reaction directed upward.

When the person rides the elevator, the acceleration is zero

            F - W = 0

            F = W

            F = 160 lb

let's find the mass of the body

            W = mg

            m = W / g

            m = 160/32

           m = 5 slug

A) when the elevator is moving up

            F - W = m a

            F = W + m a

            F - W / m = m a

            F = m (g + a)

therefore the scale reading (F) must be higher, in this case F = 180 lb

             a = F / m - g

            a = 180 - 160)/5

            a = 4 ft / s²

b) when the elevator is stopping

in this case the direction is opposite to the speed, that is to say downwards

              F- W = m (-a)

              a = W - F / m

              a = 130 -160 /5

              a = -6 ft / s²

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.