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

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

Answer 2

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`