nhluhr wrote:<slaps forehead> why don't YOU draw the diagram.
Your weight is generated by the earth's gravity, not the steps on the machine. If you don't move through this field relative to its center, your potential energy is not changing. The only work you're doing is the kinetic energy it takes to move the step-mill around and scrub off that movement as heat.
Quite simply, if you don't move relative to the gravitational field, you don't change potential energy. This is a relatively simple definition and it does NOT allow for arbitrary frames of reference other than the gravitational field. I'm sorry you don't get it, but I'm not going to waste my time drawing diagrams for something that is EASILY visualized.
A step-mill is likely to provide a smoother force curve throughout the step but do not be fooled into thinking it is in any way the same as real motion (which, after all, is the end goal here anyway).
So you think reference frame does not matter. Okay
If you only define the Center of Mass (CM) relative to the ground, then on a stairclimber the velocity of the CM is zero. And the height does not change.
In that case, you would say that the potential energy change is constant, and the kinetic energy (mv^2) is constant and zero.
So according to you, there is no change in energy. A person on a stairclimber is performing no energy moving the center of mass. Do you really believe that?
A sane person would say, hey, what if we account for the velocity of the stairclimber in the equation? Then all of a sudden, the kinetic and potential energies (and changes) make sense.
Gravity is an acceleration. The two reference frames (ground and stairclimber) differ in velocity but do no accelerate relative to one another. Gravity still acts.
Put it another way: The person standing on the stairclimber momentarily at rest moves down negatively, then pushes up and moves up positively from that lower position.