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I had a big argument at the pub about the stair machine being easier than actual stairs, and all the people there disagreed, saying that the only difference is air resistance? Are they kidding?

My point was that, as the stairs are moving in the same direction as you, you are exerting less force to maintain you torso's position; i.e. $mg = F_{\text{stair}} + F_{\text{leg}}$ (when climbing a stationary stair $F_{\text{leg}} = mg$)

The only time where this wouldn't be true is if the stair was stationary, you push yourself up, then after moving your body weight up, the stair moves down and becomes stationary again. But otherwise, the stair and your legs are moving in the same direction and the force (work?) required to work against gravity to push yourself up against the stair is less. Proof in the pudding is that, if the stairs move faster, the force exerted per stair is less

Is there a better way to explain this? It was infuriating. I think it has something to do with a work balance equation, but a figure would be better.

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    $\begingroup$ You're actually moving your center of gravity on real stairs whereas on a stairmaster you're mostly just moving your feet and your center of gravity remains more or less stationary. So less work is done. For the same thing to happen on the stairs master you would have to climb to the top of the stair master and then let the stair master take you back down before climbing up it again. What's harder? Holding onto a heavy box in place (stairmaster), or lifting it (walking)? The same reason a treadmill is easier than running. $\endgroup$ – DKNguyen Jun 4 at 23:57
  • $\begingroup$ This was my point exactly, I'm not saying your torso never moves, but the distance it moves is lesser than that of actual stairs. I was hoping to prove this numerically or by vectors. They keeps spouting about an inertial reference frame of the person means there is no difference. $\endgroup$ – Angus Keane Jun 5 at 0:07
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    $\begingroup$ Just tell them to actually do the real thing. Or do the real thing yourself and call BS on their thought experiments. The difference is super obvious after just a few steps if you're carrying a 45lbs weight. Given the same rate of rise, not difficult to show that m moving up the entire time is more work than remaining static or zig zagging up half the time and down the other half. $\endgroup$ – DKNguyen Jun 5 at 1:30
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Stair machines are not exactly equivalent to stairs for a few reasons, but not due to the fact that you stay at the same height.

In real stairs, the impact of your foot with the stair will be quite jarring (you'll use extra muscles for stabilization). The accelerations at the start and end of the step will tend to be different than the mechanics of an exercise machine. The machines may have hand bars for stability. You tend to use those in a much different way than you would a handrail in stairs.

But for the basic concept of the work your legs do, it can be similar. In the staircase your leg is exerting force to move your body upward against gravity. On the machine, your leg is exerting force to keep your body at the same height as the platform descends.

From a simplistic physics standpoint, this is very similar to walking to maintain your height on a down escalator. It takes just as much power to hold your position when that device is going down at some speed as it does to walk up a staircase at the same speed.

Is the work done walking up an escalator in the same speed and opposite direction of the escalator zero?

From a biomechanical standpoint, the way the muscles engage with the steps and the gait you use may be wildly different, leading to differences in effort and utility.

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  • $\begingroup$ " On the machine, your leg is exerting force to keep your body at the same height as the platform descends." Yes, but unlike with real stairs, you're not doing work against gravity. $\endgroup$ – Sandejo Jun 5 at 3:31
  • $\begingroup$ No you're not doing work against gravity. You're doing work against the machine. But the total work required by your muscles is identical (assuming the same tread speed, etc.) $\endgroup$ – BowlOfRed Jun 5 at 3:32
  • $\begingroup$ On a machine, you do no work on your torso, since it stays roughly stationary. On real stairs, you do positive work on your torso, since you're moving upward. $\endgroup$ – Sandejo Jun 5 at 3:38
  • $\begingroup$ That is correct. But the question didn't seem to be about doing work on the torso, but which is more difficult (effort/energy expenditure). Work done on a particular object is frame dependent. Effort expended is not. $\endgroup$ – BowlOfRed Jun 5 at 3:41
  • $\begingroup$ @Sandejo Obviously work is not associated with how "hard" something is to do. Hold a weight in the same spot for an extended period of time. Are you doing work on the weight? Is it still hard to hold the weight after an extended period of time? $\endgroup$ – BioPhysicist Jun 5 at 3:47

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