For starters, temporarily forget work and think about force. Consider an elevator.
When it starts to go up, you feel heavier as it accelerates. As soon as the elevator reaches its max speed, you feel your normal weight. If you were to climb a ladder while in the elevator, it would be no more force (or work) regardless whether the elevator is rising, falling, or motionless, as long as it’s not accelerating.
OK so far? OK, the next step is about work, and back to escalators.
It takes the whole system (you plus escalator motor) the same amount of work to get your body weight from bottom to top, regardless of how much work you do and how much the escalator does. (For now I’m ignoring the effort you expend standing still or jogging in place or whatever. Just looking at the work obtained from the system.)
If you do no work at all, the escalator motor does it all. If you hoof it, you end up doing some portion of the work. If the escalator motor is off, you do all the work. In all cases, same total of work (or, more specifically, work output).
That’s true even if the escalator is going down. However, if the escalator is going down so fast you can barely keep up (trying to go up), obviously, you’ll burn more calories (and “do more work”) to get to the top. There’s no difference in total work output of the system, but you wasted a lot of effort in inefficient motions. To this extent, sbunny8 is clearly correct.
But let’s ignore that too, because we’re talking about two relatively efficient cases: walking up a stopped escalator versus walking up a moving escalator (moving in the desired direction).
The power required to get started on the moving escalator is greater, for the same reason you feel heavier when an elevator starts. But once you’re going, the power requirement is the same whether the escalator is moving or not. When you get off at the top, you get that difference in power back, so that’s a wash.
The difference is you get to the top more quickly on the moving escalator, so it takes YOU less work. (Work = power * duration)
Originally the OP was comparing stairs versus escalators. It’s better to compare a moving escalator versus a stopped one, to discount differences in effort due to the riser height. If the OP thinks that it’s more work to walk up the moving escalator, I believe that’s a mistaken impression, for the reasons cited above. It takes more power to get started, but after that the power requirement is the same, and the duration is shorter, so it’s far less work.
And I’m pretty confident that the power is the same, because we don’t feel heavier in an elevator, once it gets to full speed, even the really fast ones. Chronos knows this because he understands physics. It would have been my first guess, but I’m far less confident of my grasp of physics!
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