Question

Karen has a mass of 57.9 kg as she rides the up escalator at Woodley Park Station of the Washington D.C. Metro. Karen rode a distance of 69.6 m, the longest escalator in the free world. The acceleration of gravity is 9.8 m/s 2 . How much work did the escalator do on Karen if it has an inclination of 34.8 ◦ ? Answer in units of J.

Answer 1

Answer:22537.92 J

Explanation:

Given

mass of karen $\left ( m\right )=57.9 kg$

Distance covered by Karen =69.6 m

acceleration due to gravity=9.8

inclination$=34.8^{\circ}$

vertically karen move

$h=69.6\times \sin \left ( 34.8\right )$

h=39.72 m

Work done by escalator on karen is equal to change in potential energy of  karen

$\Delta P.E.=m\times g\times \Delta h$

$\Delta P.E.=57.9\times 9.8\times 39.72=22537.92 J$

Answer 2

Answer:

22537.92 J

Explanation:

We are given that

Mass of Karen=57.9 Kg

Karen rode  a distance=69.6 m

Acceleration due to gravity=$9.8 m/s^2$

$\theta=34.8^{\circ}$

We have to find the amount of work done by escalator on Karen.

Vertical height of longest escalator=$69.6 sin 34.8^{\circ}=39.72 m$

Work done=Potential energy of escalator

Work done=mgh=$57.9\times 9.8\times 39.72=22537.92 J$

Hence, the work done on Karen=22537.92 J