# Does a moving escalator make it easier to walk up the steps?

I was discussing with my colleagues why it feels easier to walk up an escalator when it is moving. My natural assumption was that the movement of the escalator imparts some extra acceleration on the rider that helps to move up the stairs. But my colleagues insisted that this was nonsense, and that the affect is purely psychological (i.e. it just seems easier).

We actually came up with three contradictory hypotheses, and I'm not sure which is right: 1. The escalator is constantly accelerating the rider since without constant acceleration the body wouldn't be able to counteract the force of gravity (i.e. my theory). 2. The rider is not accelerating since no acceleration is needed to maintain a constant velocity. 3. The acceleration of the escalator actually makes it harder to get to the next step since it pushes the rider against the current step.

Which of these is correct?

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Compare to What's the difference between running up a hill and running up an inclined treadmill?. Personally I doubt that it is easier (or harder, it's roughly a inertial frame), which would imply that the sense of motion is fooling you into feeling that it's easier. –  dmckee Jan 17 '12 at 18:39
It is possible that the act of bouncing against the stairs as you run up makes the escalator go backwards a little at each step, pulling the stairs down a little. Without such an effect, there would be no change. –  Ron Maimon Jan 18 '12 at 5:19

Number two is correct:

2.The rider is not accelerating since no acceleration is needed to maintain a constant velocity.

The first option offered:

1.The escalator is constantly accelerating the rider since without constant acceleration the body wouldn't be able to counteract the force of gravity (i.e. my theory).

Here's why that's wrong.

To apply Newton's second law, $F = ma$, all system forces and their interaction must be taken into account. If you hold an object in the palm of your hand, you are applying some force on that object, but that object is not accelerating and it's not even moving. This is because the force you apply on that object is equal and opposite to the force of gravity.

In the case of an escalator, a motor provides some torque (rotational force) which is acting agianst forces of friction in the system and gravity which weighs down the passengers. After all forces are taken into account, the velocity of the escalator is (approximately) constant therefore the acceleration is zero and walking up those stairs is no easier than walking up a regular set of stairs.

Walking up the stairs of an escalator may even be more difficult than walking up a regular set of stairs because increased velocity relative to the surrounding atmosphere causes an increase in fluid friction acting on the walker.

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Once you get yourself moving, the escalator does not accelerate you and does not assist your running up hill. The only advantage an escalator gives you is that you keep moving up even if you don't put any effort into it.

Next time you feel like running up an escalator (which is not entirely safe), you might consider repeating the experiment with your eyes closed. That will eliminate the visual effect but you will still feel the air flow on your face.

This is basic Newton's law on inertial frames. You cannot detect steady motion. This is why you can throw dice in the gambling compartment of a luxury airliner that is moving at 400 miles per hour. Or why you can exist on the earth's surface without realizing that it is moving (due to the earth's turning) at an even faster rate (depending on latitude).

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