In gyms I sometimes work out on a stair climber machine. This machine has stairs that move down and you have to climb upward to stay on the machine. I've taken a high school physics class, and I was thinking, since your body stays in the same position, only your legs have to move down, is it possible to cheat the stair climber and do it using little energy? I know this wouldn't be possible for a human, but would it be possible for a machine? Without leaning on the rails.
Suppose there are two conveyor belts, A and B. You're standing on A. You notice that B is moving relative to A.
Question 1: Is it possible to let B go by without doing any mechanical work?
Answer: Yes, just let B go by without touching it.
Note that it doesn't matter whether A is really moving or standing still, or whether B is really moving or standard still, or both/neither. We can't say whether things are "really" moving.
Question 2: Is it possible to be in this situation, and make a force on B in the direction of B's motion relative to A, without doing work?
Answer: No. Work equals force times distance.
If you replace "conveyor belt A" with "the rails," then your question is question 2.
Assume a stair climbing machine of the sort that resembles a short, pointless escalator. Such a machine is, perforce, getting more or less constant force applied to it. Because the stairs constantly go down, that force is exerted over a distance (unless you cheat and hang on the rails).
The sort of "stair climber" that features a pair of steps that are geared so that one rises as the other falls could theoretically work so that no energy is absorbed -- but only if the machine is specifically designed not to absorb energy (i.e., designed without drag, so it always pushes up on the rising tread with the same force as is being exerted on the falling tread).
Again (probably) no.