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 it. The scale reads 150 lb as the door closes. The reading varies between 120 lb and 170 lb as the elevator travels 101 floors.

i)What is the maximum acceleration upward?
ii)What is the maximum magnitude of the acceleration downward

(i) The maximum acceleration upward is 2.02 m/s².

(ii) The maximum acceleration downward is 1.39 m/s².

Explanation:

Let a be the maximum acceleration of the elevator.

The mass of the person at ground is 150 lb. We have to convert the mass into kg,

1 lb = 0.453592 kg

150 lb = 68 kg

170 lb = 77 kg

120 lb = 54 kg

(i) The person experience a force due to Earth's gravity in the downwards direction. The magnitude of this force is:

F₁ = mg = 68 x 9.8 = 666.4 N

The weight of the person decreases as the elevator is moving upwards. So, the force experienced by the person in this case due to gravity is:

F₂ = 54 x 9.8 = 529.2 N

Applying Newton's force equation;

(F₁ - F₂) = ma

(666.4 - 529.2) = 68 x a

a = 2.02 m/s²

(ii) The weight of the person increases as the elevator is moving downwards. So, the force experienced by the person in this case due to gravity is:

F₂ = 77 x 9.8 = 754.6 N

Applying Newton's force equation;

(F₁ - F₂) = ma

(666.4 - 754.6) = 68 x a

a = -1.30 m/s²