It must be, right? Obviously, if you're pushing a block by exerting a force F on it over a distance D on the ground, if you are in the frame of you or the block, your distance is 0 so it appears you're doing no work. I ask this question because I was doing a practice problem that should be really simple, but is bugging me. In it, there's a guy (mass m) in an elevator, which is accelerating upwards at constant acceleration a. At the given moment, its speed is V. It's easy to show that the normal force on him is F = mg(1 + a/g), which makes sense. But then they say that he now has a ladder in there, and is climbing up at a constant velocity v, and ask what his power output is. Naively, I say it's just P = Fv. However, the answer says P = F(v + V). This seems wrong for several reasons to me: a) If we look at the limit v = 0 (he's just sitting there, not climbing), it says he's still burning energy, and b) In the limit of a = 0 (the elevator is going up at a constant speed), he shouldn't be able to tell he's even in an elevator as opposed to a stationary room, so it should definitely degenerate into mgv, not mg(v + V). It seems like extra energy he'd have to expend climbing the ladder when a =/= 0 is included in F. Can anyone illuminate this for me?