Since the change in kinetic energy is still zero, this means that the positive change in gravitational potential energy is equal to the negative of the change in internal energy. Let’s say you have a mass of 75 kilograms (165 pounds). That means moving up 1 meter would reduce your internal energy by 735 joules. That’s called working out.
Climbing Stairs vs. a Stair Climber
Now we can go back to the original question: What does the work-energy principle say about stairs versus a stair-climbing machine? Well, we already did the physics of stair climbing. It’s the same calculation if you get on top of a 1 meter table or climb 100 stories—it’s just a different value for the height. But suppose you stay in the same place while the stairs move under you. If someone is measuring your forward motion, they’d say your speed is zero. Your height also doesn’t change, so now the work-energy equation looks like this:
This says the change in internal energy is also zero, which means you don’t burn any calories. I mean, that can’t be right … right? Then how do we fix this? I’m going to use a nice example based on this video from Steve Mould. It goes like this: Imagine you are climbing up a downward-moving escalator. Again, an observer on the ground would see you as stationary. However, we could also measure your speed from the reference frame of the escalator, and you would be moving up.
In fact, if the escalator had walls and a ceiling, you wouldn’t be able tell that you were staying in place. You wouldn’t even know the stairs are moving. Since the stairs are moving at a constant velocity (zero acceleration), this would be an inertial reference frame. In physics, any inertial reference frame is as valid as any other reference frame—the basic laws of physics remain the same. So, from the perspective of the escalator frame you are moving up and doing work. It’s the same as if you were walking up a stationary frame.
But Actually, the Stair Climber Is Harder
I said that the stair climber and climbing stairs were the same—but they are not. In fact, climbing up 100 stories is easier than the equivalent distance on a stair climber. Does that seem crazy? It is a little crazy. The reason they’re different is because the gravitational field (g) is never really constant.
Remember, we defined the gravitational potential energy as U = m x g x y? That’s not really wrong, but it is a little misleading. Actually, the gravitational potential energy for the Earth-person system would be defined as the following: