Earlier this week, I wrote about an inclined treadmill, and talked about physical work. Physically, the amount of work that you do is equal to the amount of force that you exert in a certain direction multiplied by the distance you move in that direction.
If you walk up an incline, as opposed to moving on a level surface, you have to also fight the force of gravity to get up that hill, hence you have to do extra work.
I contended that, in order to walk up an inclined treadmill, you also have to do extra physical work, the same way you have to do extra physical work to walk up a real hill.
“Not so fast,” said many of the commenters! Unlike a real hill, where you actually wind up at a higher elevation than you started at, you don’t travel any real distance on a treadmill, and you certainly don’t end at a different elevation than you started at! Therefore, the argument goes, you don’t do any extra physical work.
So, I ask you, what would Einstein have to say about this? Einstein — mastermind of the equivalence principle — realized that as far as forces go, the only thing that you feel is acceleration. Your environment doesn’t matter at all.
What’s a good, analogous thought experiment for our treadmill/hill problem here? Imagine an escalator. Now, you’re going to walk up this escalator, and you’re going to walk up 50 steps on this escalator for three different cases, like Fred here.
If you walk up 50 steps, and each step is 0.2 meters high, then you will raise your elevation by 10 meters relative to not taking those 50 steps. In other words, it doesn’t matter whether that escalator is moving up while you do it, in which case you might wind up raising your elevation by 20 meters total, or the escalator is moving down, in which case you might wind up not changing your elevation at all.
In either case, you have to do work against the force of gravity, regardless of what your velocity is. This even works in the case of a broken escalator, a.k.a. stairs.
And that’s why, regardless of whether your elevation changes or not, you do work whenever you walk up an incline! Hope you’ve had a great week, and I wish you all a great weekend!