If you just stand still on an escalator (moving stairway), it takes 20 seconds f

Question

If you just stand still on an escalator (moving stairway), it takes 20 seconds for it to carry you up one floor, about 5 meters. But if you walk up, you get to the top of the escalator in only 12 seconds. (a) How mu Ch work does the escalator do in lifting you up to the next floor, it you just stand there? (b) How mu Ch if you walk up? (c) Some people expect the answer in part (b) to be the same as in part (a), saying that the escalator is still exerting the same force over the same distance; some people expect it to be more, saying that when your walk up your feet press down harder on the stairs than the do if you just stand, so the force is greater; and some people expect it should be less, saying that you're expending energy, so the escalator must expend less. Explain the problem with the reasoning by the folks who have it wrong.

Explanation / Answer

a) You are just standing on escalater, so you are not accelerating (moving with speed of escalater) and the net force on you must be zero. Something must be canceling your weight, which pushing you directly upward with a force that is equal in amount to your weight.

b) You are moving at constant velocity on the escalater, so you are moving with sum of velocities (escalater+ your velocity). so that escalater need to do less work when compared to 1st case.

c) gravity always works perpenducularly down wards and acceleration is applied inclid to the plane.

in the 1st case weight of the person= component of force of the escalater

in the 2nd case weight of the person= component of force of the escalater+ component of force by the person.

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