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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.

User Eric White
by
5.4k points

2 Answers

4 votes

Answer:

22537.92 J

Step-by-step 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* 9.8* 39.72=22537.92 J

Hence, the work done on Karen=22537.92 J

User Kacper Polak
by
5.3k points
0 votes

Answer:22537.92 J

Step-by-step 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* \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* g* \Delta h


\Delta P.E.=57.9* 9.8* 39.72=22537.92 J

User Steve Wilford
by
5.3k points