Question

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 140 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?

Answer 1

To develop this problem we will proceed to convert all units previously given to the international system for which we have to:

$140 lb = 63.5 kg \rightarrow 63.5kg (9.8m/s) =622.3 N$

$120 lb = 54.4 kg \rightarrow 54.4kg (9.8m/s)= 533 N$

$170 lb = 77.1 kg \rightarrow 77.1 kg (9.8m/s) =756 N$

PART A ) From the given values the minimum acceleration will be given for 120Lb and maximum acceleration when 170Lb is reached therefore:

$F = 756 - 622.3$

$F = 133.7N$

Through the Newtonian relationship of the Force we have to:

$F= ma$

$a = \frac{F}{m}$

$a = \frac{133.7}{63.5}$

$a = 2.1m/s^2$

PART B) For the maximum magnitude of the acceleration downward we have that:

$F = 622.3 - 533$

$F = 89.3N$

Through the Newtonian relationship of the Force we have to:

$F= ma$

$a = \frac{F}{m}$

$a = \frac{89.3}{63.5}$

$a = 2.1m/s^2$

$a = 1.04 m/s^2$