A 65 kg shopper in riding an up-going escalator, which has an incline of 31 degrees with respect to the horizontal. It is moving at 6 m/s. The top of the escalator is 24 m above the ground.

Required:
a. Calculate how much work is done by the friction force between the shoes of the shopper and the step of the escalator as the shopper moves from the bottom to the top of the escalator.
b. Calculate how much work is done by gravity for the ride from the bottom to the top of the escalator.
c. Calculate the potential Energy the woman has at the top of the escalator.

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roccokarr2020 roccokarr2020 · Answer 1 · 2021-06-25T17:49:45+02:00

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onyebuchinnaji onyebuchinnaji · Answer 2 · 2022-06-22T14:12:38+02:00

(a) The work done by the friction force between the shoes of the shopper and the step of the escalator is 15,266.2 J.

(b) The work done by gravity for the ride from the bottom to the top of the escalator is 13,104.5 J.

(c) The potential Energy the woman has at the top of the escalator 15,288 J.

The work done by friction force is calculated as follows;

W = μFn x d

W = (tanθ)Fn x d

W = (tanθ) x mgcosθ x L

W = (tan 31) x (65 x 9.8 x cos31) x h/sinθ

W = 0.6 x (546.02) x 24/sin31

W = 15,266.2 J

W = Fₙ x h

W = mgcosθ x h

W = (65 x 9.8 x cos31) x 24

W = 13,104.5 J

P.E = mgh

P.E = 65 x 9.8 x 24

P.E = 15,288 J

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