Karen has a mass of 56.2 kg as she rides the up escalator at Woodley Park Station of the Washington D. C. Metro. Karen rode a distance of 60.4 m, one of the longest escalators in the 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 28.9 ◦?

Question

Physics

Joey Howe

19 August, 19:33

Karen has a mass of 56.2 kg as she rides the up escalator at Woodley Park Station of the Washington D. C. Metro. Karen rode a distance of 60.4 m, one of the longest escalators in the 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 28.9 ◦?

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Answers (1)

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Patton · Answer 1

W = 16.08 kJ

Explanation:

mass of Karen = 56.2 Kg

distance Karen rode (l) = 60.4 m

acceleration due to gravity = 9.8 m/s²

inclination of escalator with horizontal (θ) = 28.9◦

work escalator = ?

height at Karen has moved

h = l sin θ

h = 60.4 x sin 28.9°

h = 29.19 m

Work done = Δ PE

Work done = m g (Δ h)

Work done = 56.2 x 9.8 x (29.19 - 0)

Work done = 16076.68 J

W = 16.08 kJ

Work done by the escalator is equal to W = 16.08 kJ