You’d have to crawl a massive flight of stairs to have any noticeable weight difference in yourself… I do believe climbing a set of stairs at a certain rate would be the same amount of work as staying in the same place on an escalator moving at the same rate.
After all, i’m sure the work equation doesn’t take into account the frame of reference moving (the escalator stairs).
Here seems to be a related discussion: International Skeptics Forum
Considering a simpler case may be of use.
Imagine, instead of an escalator, a treadmill (yes, yes, I know. No airplanes, thankyouverymuch) tipped at an angle. Imagine this treadmill is completely frictionless, and starts at rest.
Now, imagine you step onto the treadmill at the top. What happens? Your weight will have a force component along the direction of the treadmill. This means your weight will accelerate the treadmill. By the time you get to the bottom, you will transferred energy, equal to mgh, to the treadmill. Transferring energy means doing work. This work goes into kinetic energy of the accelerating treadmill.
Now imagine you can run at lightning speed. As soon as you reach the bottom of the treadmill, you run to the top and ride down again. In this case, the total energy you’ve imparted to the system is 2mgh.
Now imagine your friend (who weighs the same) is a slow plodder. He steps onto the top of an unmoving treadmill. It starts to move downward. He immediately turns around and plods upward, but is never able to reach the top. In fact, he slowly drifts to the bottom, and steps off the bottom in exactly as much time as it took you to ride down once, zip to the top, and ride down a second time. How much energy did your buddy transfer to the system?
Well, he applied the same force for the same length of time–he must have accelerated the treadmill up to the same velocity…which means he imparted the same energy, 2mgh.
Don’t like the accelerating treadmill? OK the, imagine a magical device that keeps this treadmill going the same speed, no matter what, by adding or removing energy as needed (in real life, we call this magical device an “electric motor”). Everything above still applies: ride it down once and you’ve applied energy equal to mgh. Ride it down twice and you’ve applied energy equal to 2mgh. The magical device removes the extra energy as quick as you apply it.
More importantly, if you stay on it for the same length of time it takes to ride down it from top to bottom, you apply energy equal to mgh. It doesn’t matter if you stay put in one place, plod slowly upwards, or quickly climb so as to stay the same height above the ground. You still impart the same energy. In one case the energy ultimately comes from gravity, in the other it comes from your muscles.
Finally, note that if you climb the treadmill so as to stay the same height above the ground and your lazy buddy just rides from top to bottom without walking, you would have “walked” exactly the length of the treadmill in the time it takes your buddy to go from top to bottom. In otherwards, your muscles “feel” like you’ve climbed up to a height of h…because that’s the amount of energy they’ve expended.
Fuzzy questions usually result in fuzzy answers. Your question assumed knowledge of the circumstances of “The Biggest Loser” program which I seldom watch more than a minute or two of.
The work that you do is the force, your weight, times the vertical distance you travel with respect to the escalator, i.e. the number of treads times their individual height.
It makes no difference that the escalator is moving, up, down, or not.Comparable to a very long/high flight of stairs.
The treadmill is similar as you are walking up an inclined plane. You stand in one place and in effect climb a short vertical distance with each step depending on the angle the machine is set on.
Hope that clarifies things for you.
Try one of these stairclimbers for 20 minutes at a steady pace and tell me if your doing any work.
It entails much more than just lifting a leg to the next step. While you’re lifting one leg into the air the other is bent and flexing back to straight while supporting all of your weight.
Climbing up a down moving escalator should be just like climbing a set of stairs, except the escalator keeps returning you to where you started.
Start with a person on a down escalator. Person stays in the same place by climbing the escalator. Now turn off the escalator. What happens? The person, with the same amount of work climbs the escalator/now-stairs. So did the escalator being turned off suddenly cause the person to start working, or was the escalator applying a downward vector on the person and that has now been removed?
Though your body stays in the same place, it’s a mistake to think that no work is required to keep it there. Yes, there’s that “a body at rest tends to remain at rest” thing, but gravity is relentless. If you step off a chair, your “remaining at rest” will be only a brief instant before gravity takes over. The escalator is continuously pulling the chair out from under you, so you are continuously working against gravity.
So, if you’re looking for an exercise to compare it to, it’s more like half-squats than knee lifts. That is, you stand straight, then bend both knees to lower your body by the height of one escalator step, then stand straight up again.
Besides that, I believe your definition of work is not broad enough. Let’s say there’s two steel beams a yard apart, with a hydraulic cylinder in between them. Start with no pressure in the cylinder. Then switch on the pump, and apply pressure to the “extend” side of the cylinder to the point where 300 pounds of force is pushing from one beam to the other. Now, shut down the pump and bleed down the pressure. Neither the cylinder nor the beams moved at all. Was work done? Yes. Energy was used to compress oil. You could hear the pump bearing down.
Now, take out the cylinder, and stand between the beams yourself. Push as hard as you can against the beams for two minutes. Again, no motion took place, but your muscle fibers tightened and generated heat, your pulse rate went up, and you began to sweat. Energy was consumed, and effort was exerted against a pair of stationary objects. Work was done. That’s how I see it, anyway, in my non-tech way.
On an elevator travelling at constant speed you weigh the same as when standing outside the elevator waiting for it to arrive. You weigh less when the elevator accelerates from standing still to its maximum speed at the start of descent, and more when it decellerates back to standing still at the end, but in between you weigh the same.
Other than that, your elevator analogy is a good one and should help the OP understand what’s going on. By similar reasoning we ignore the fact that the earth is travelling through space (relative to the sun) and rotating when we look at the simple stair climbing case.
When on the escalator you are moveing your legs up from a lower step to a higher one which requires the expenditure of energy. That seems to me the same amount of energy that is required to move you legs from one step to a higher step on a stairway. However, on the stairway you are also moving your mass to a higher energy state relative to the ground and on the excalator you are not.
Takes more energy to climb the stairway.
Your position relative to the ground is irrelevant. Work is performed against the force of gravity, whether you are moving up, down or not at all.
My position relative to the ground determines how far I am from the center of the earth. When I am at the top of the stairway I am further from the center and have increased my potential energy. When I “walk up” the down escalator I have not added that energy.
On the escalator I merely have to lift my leg to the higher step. On the stairway I have lift my leg to the higher step and push hard enough to also lift my body further from the center of the earth.
Yes, I’m not sure what I was thinking when I posted that you were lighter on a down-moving elevator, since it actually invalidated what I stated in my first post (which I still believe) – that in the frame of the escalator, you’re just climbing stairs.
In any event, since this is GQ, I agree with DanBlather and the couple of other folks who said I was wrong on the lighter/heavier in an escalator thing. And my high school physics teacher can stop slapping his forehead now.
That would be true if you stood at the end of down escalator (i.e., on the stationary floor) and just lifted you foot up and rested it on a moving stair. When you are on the escalator you and the escalator are moving at a constant speed. To move relative to the escelator you need to exert exactly the same force you would need to climbe an equivalent stair on a stairway.
I don’t think so, but I suppose I could be convinced otherwise.
The way I see it, if you are going up a down escalator and just going fast enough to stay in one place in the gravitational field of the earth you merely need to exert an upwar force equal to your own weight. Just as if you were merely standing still with the added exertion of lifting your legs. When you are going up a stairway you must support your own weight, exert the energy to move your lets and in addition you must apply enough added energy to increase your potential energy.
Or more simply, in both cases you are climbing the stairs but in one case you are increasing your potential energy and in the other you are not.
When you climb a down escalator you are increasing your potential energy relative to the stairs you leave behind There is nothing magic about the frame of reference of the store. Imagine that the escalator was stationary and the store was moving. That is exactly the same as if the escalator is moving and the store is standing still.
What about your potential energy relative to the stairs that are leaving you behind? Both you and the stairs as a whole are standing still.
I have no idea what you mean.
You are gaining potential energy relative to the steps that are going down because you are stationary with respect to the gravitational field while the steps going down are decreasing their potential energy. However, there are also steps that are rising against the gravitational field and they are gaining potential energy at the same rate as the down steps are losing it. The moving stair as a whole is maintaining constant potential energy because its parts are always at rest with respect to the gravitational field. And if you are walking up the down stairs at the same rate that the stairs are going down you are not changing your potential energy either.
The directions in the gravitational field of the earth are not symetrical. There is an up, or against the force of the field and a down or with the force of the field. Motions with or against the field are not symetrical. I don’t believe that it is legitimate to use the stairs as your reference in the gravitaion. If you call the down going steps zero potential energy then everything else on earth, including the earth itself, is gaining potential energy.
When you are on the escalator you are not going either up or down. When you go up a a stairway you are going agains the field and doing extra work.
And I leave it at that.
This is getting really intersting. I hope someone with a formal physics background chimes in. There are several questions here:
Work can be converted to potential energy, as when you walk up stairs.
Let’s try a different tack. Suppose we have a two story building with the second floor 10 ft above the first. In the room on the first floor there is a stairway on one side going up to the second story. On the other side is a down excalator also going up the the second floor. You and I both weight 200 lb. and you start up the stairs at the same time as I get on the escalator. Further suppose we take steps at the same rate and of the same height and the pace of the escalator is such that I stay in the same place. When you reach the second floor I get off the escalator. Say the first floor is our reference potential energy of zero.
You have lifted your 200 lb. (exerted a 200 lb. force) through 10 ft. and have done 2000 ft. lb. of work. I am now still at zero potential energy and you being 10 ft. above me are at 2000 ft. lb. We have both negotiated the same number of steps but you have gained 2000 ft. lb. and I have gained none. So you had to exerrt more energy than I did.
This assumes that I do no work in making the escalator go. And for a frictionless system that’s the case, even if it’s not self powered, because the stairs going down the escalator lift the stairs that are returning to the top and all I need do is overcome friction, which is assumed zero, or at least very small.
This is true no matter where we place the reference point for potential energy. Suppose we color one step on the escalator red and it is an endless, powered escalator. The red step is our zero energy reference point. If the experiment is repeated you still finish 10 ft. higher than I do. When I am 100 ft above the red step and have 20000 ft. lb of energy relative to the step, you are 110 ft. above it and at an energy level of 22000 ft. lb. relative to it.
If a person goes up a stairway he gains height relative to one who stays at the same level on the escalator. It is evident then that he has gained energy relative to the other and so must have exerted more energy.
