Question

An escalator carries you from one level to the next in an airport terminal. The upper level is 4.7 m above the lower level, and the length of the escalator is 7.0 m . Assume that your mass is 61 kg .
A. How much work does the up escalator do on you when you ride it from the lower level to the upper level?
B. How much work does the down escalator do on you when you ride it from the upper level to the lower level?

Answer 1

Answer:

2812.66685 J

-2812.66685 J

Explanation:

m = Mass of person = 61 kg

L = Length of escalator = 7 m

h = Height of escalator = 4.7 m

The angle between the normal force and the distance traveled by the person would be

$\theta=cos^{-1}\frac{h}{L}\\\Rightarrow \theta=cos^{-1}\frac{4.7}{7}\\\Rightarrow \theta=47.82^{\circ}$

Work done is given by

$W=mgLcos\theta\\\Rightarrow W=61\times 9.81\times 7\times cos47.82\\\Rightarrow W=2812.66685\ J$

The work done by the escalator on the when the person rides it up is 2812.66685 J

While going down the angle will be

$\theta=180-47.82\\\Rightarrow \theta=132.18^{\circ}$

$W=mgLcos\theta\\\Rightarrow W=61\times 9.81\times 7\times cos132.18\\\Rightarrow W=-2812.66685\ J$

The work done by the escalator on the when the person rides it down is -2812.66685 J