Are you saying that as he climbs farther from the center of the earth the person on the stairs weighs less than the person on the elevator? That is certainly true, but if I calculate it correctly it is about 0.00004% difference after 9 feet. So yes, the amount of work is very slightly more for the person on the escalator.
I dont really think that’s the umpteenth time someone’s stated the problem like that, it only seems to be since you’ve realised you’re flogging a dead horse with your no-work argument and re-worded the problem to fit it.
If you really want to talk about lifting your CofG then we can consider the whole setup an inertial reference frame, within which your CofG is being raised and GPE gained. We dont need to go that far, however, since the work being done doesn’t need to be thougth of as lifting of CofG, it’s work done in moving two bodies away from each other against a constant force (mg). That’s the same in the stairs and the escalator case and I’m pretty sure it means the same work (near enough, all other factors being equal) will be done in both cases.
Enough straws there…? (said with jest, not sure if that counts as an insult in GQ, if it does, I apologise)
You’re right about the whole gravitational field getting slightly weaker as you climb the stairs, and I had thought about this when considering the problem, but thought we’d all silently agreed that the difference is so trivial (5m rise compared to ~6.4x10[sup]6[/sup]R[sub]e[/sub] that it didn’t even deserve a mention.
Can we all agree to neglect the f=Gmm[sub]e[/sub]/r[sup]2[/sup] when we’re talking about work here? Gives everyone a chance to re-think it and change sides if you realise that the other argument is correct.
Right and as soon as I posted it I realized that the reason you must do work in climbing the stairs with a moving gravitational field isn’t that. The stairs are moving with the field so that the force pushing the person into the stair is equal to his weight. The reason more work is done in this case is the same as the stationary field case. You are moving a mass upward relative to the field.
In what post is my “no work argument?”
And here is the question asked by the OP in post #3
How did I change it to fit a “no-work argument” that I don’t remember making?
This is pretty sketchy. What two bodies are being moved away from each other in the stairs case and what two in the escalator case? Could you deign to stoop down and explain a little? If you don’t want to take the time I’ll understand.
But please eschew the giant wheel.
Not what I meant.
I’m not saying “while you are physically on the escalator, you are doing work” (although that’s true). I’m saying, “in this case energy is being transferred from you to the escalator.”
That’s the difference between the stairs and the escalator. On the stairs, the work you do goes toward increasing your potential energy. On the escalator (assuming you’re walking in place), the work you do goes into the escalator, either by accelerating it (in the freewheeling case) or reducing the power input required from the motor (in the motorized case). In either case, it’s the same amount of work.
Maybe Mr Simmon’s points can be adressed if we view the project upside-down.
Imagine a child hanging from his hands on an inverted monkey bar conveyor. If the conveyor is stopped the child can only physically climb 20 monkey bars till fatigue sets in and the child lets go. The child has also climbed a certain distance higher off the ground.
If you start the conveyor (at the same rate the child can climb) in order for the child to remain in place he has to work to raise himself to the next bar and grab it, - each time. He exerts the same work to bend the arm and grab the next higher bar even though he is hanging motionless relative to outside observers. He is still fighting the same gravitational forces as if the bars were motionless and he will still only be able to climb 20 bars this way before fatiguing and falling off.
Just because he hasn’t raised himself further off the ground does not mean that any more or less work was being performed.
Apologies for the slightly snarky comments earlier. Bit I guess I can stoop a little now (please excuse any horrible spelling errors, i’m surfing via iPaq and bluetooth phone while I’m on a 9hr train journey, i’ll be back online properly this evening).
Quote:
If you really want to talk about lifting your CofG then we can consider the whole setup an inertial reference frame, within which your CofG is being raised and GPE gained.
I’ve got no idea where my head was at there, it’s quite clealy false. Doesn’t affect the rest of what I’m saying, though. Sorry for that bit.
In terms of forces it doesn’t matter that each step is connected, so let’s pretend they’re not. With every step you take, you exert a downward force on the step. As you do this, the distance between your CofG and the step is increased, hence two bodies moving apart. Doesn’t matter how they move WRT to anything else, you applied a certain force, you moved something a certain distance.
I know you’re not the biggest fan of my fanciful thought experiments, but turn the whole situation upside down and give the escalator assembly your mass. You’re carefully balanced on your hands and skillfully got the escalator centre steps on the soles of your feet (I’d be impressed). Assuming you can keep the whole lot upright, in order to stop the ‘down’ escalator (whose steps with your feet on are now staying stationary, moving the escalator down) at the same height,you’ll have to ‘walk’ upward, each step you take pushing against a force equal to your weight.
In this case, once again, nothing moves WRT to the ground but you’d do the same work because with each step you’re overcoming the same force over the same distance. You’d get a lot more tired this way, though.
I’m not sure we’ll ever agree on this because maybe we’ve got conflicting ideas of work and I’ll bow out if mine’s wrong. Work Done = force x Distance moved in the direction of the force. I didn’t think that where energy goes factored in to tnis. But I may be wrong.
Aha, this is a good point. First off, the OP’s question was is it harder for a person to walk upstairs or to walk fast enough to stay stationary on a down escalator. The only work that counts is that resulting from the person’s exertions. His weight on the escalator puts energy into the machine and its motor doesn’t have to work as hard as without that weight. However that work is not the result of the person’s exertion. That work is a result of the pull of the gravitational field and would be the same even it the person just stood there. The work that the person puts into the machine arises from the impulses that occur when he accelerates a leg to lift it and take a step and again when the leg’s motion is stopped when foot returns to the escalator. It seems to me that that same work occurs when your are on the stair. That is, the exertion of the person is not putting any more work into the escalator than is being put into the stair. However, the weight of the person on the stair does have a great effect on the work done by that person since the weight has to be lifted. What say you?
Just to be clear, we need to draw a line between “work” in the strict physics sense and “work” in the sense of simply exerting oneself. Work in the physics sense requires force and displacement. So, as an obvious example, pushing against an immovable wall does no total work (no displacement), even though it requires exertion. As a not-so-obvious example, lifting and returning a barbell does no total work. Just lifting the barbell requires work-- you change the potential energy. But returning the barbell is an energy flow in the other direction, so the total work is zero. Even though you’re still exerting, the barbell is doing work on you during the return.
OK, that being said…
I agree with all of that, but…
I might disagree with this, depending on exactly what you mean. Let’s look at four cases:
Case 1: Standing on the stairs. The stairs are not moving, and neither are you. No energy is transferred, and no work is done. (As an aside, you could be jumping up and down and exerting yourself, but you’re not doing total work.)
Case 2: Walking up the stairs. The stairs are not moving, but you are. Your body gains potential energy, so your muscles are doing work to lift yourself to the top of the stairs.
Case 3: Standing on the “down” escalator. The escalator is moving; you’re standing still compared to the escalator but moving with relation to the ground. Your body loses potential energy. That energy must go somewhere; it goes into work on the escalator (force * distance traveled). From there, the added energy decreases the motor current needed to drive the escalator (or maybe even reverses the current; who knows?)
Case 4: Walking up the “down” escalator at the same pace the escalator goes. The escalator is moving; you’re moving compared to the escalator but standing still with relation to the ground. You’re neither gaining nor losing potential energy in this case. However, you are still applying a force on the escalator, and the escalator is travelling. That’s work. The work comes from your muscles and ends up in the escalator.
And with a quick calculation, you can show that the work in Cases 2, 3, and 4 are equivalent.
This of course focuses on the physics definition of “work” as opposed to the exertion definition. However, I see no reason there would be any difference in exertion between Case 2 and Case 4. And I think this answers the original question by the OP, who was focusing on the physics definition.
No. You and many others on the thread are treating work as a vector quantity, which it isn’t. The total work is independent of discrete path or direction.
The barbell is doing no delta return work on you during its descent, the potential energy from the prior lifting is not recoverable by your body. Additional work is still being done on the descent in the form of internal friction within your muscles. You are accelerating a mass a certain distance upwards (positive work), and then are decelerating a falling mass as it descends (still doing positive work).
This entire scenario is dependent upon how reversible the work transfer is within the system. Work transfer between you and the barbell is entirely one-way, and all of the work (potential energy) that the barbell is trying to return to you mechanically is lost forever within your body as heat.
If the total work is independent of discrete path and direction (which it is) and the barbell starts and ends in the same place (which it does), then the total work is the same as if the barbell had never moved: zero. Which is what I said, and you disagreed with. I’m puzzled at how you come to a different conclusion.
But the energy goes somewhere. It doesn’t return to your muscles (and does, as you say, get burned as heat), but it does leave the barbell.
The OP is concerned with how tired you get. Any time you, yourself, move your body or any part of it laterally or up you are doing work. You are either lifting a mass or giving one kinetic energy.
As to the wall I think the proper way to look at it is that you are not doing any work on the wall. However you body is doing actual work, your heart rate speeds up and so you are moving a mass of blood faster. Its kinetic energy is increased and the muscles in you heart are moving faster and so have more kinetic energy which they got by work being done. If you push hard enough to develop tremor in your arms the muscles slide over one another against the frictional resistance and so a force is exerted over a distance. I believe any physical activity that results in an increase in you metabolic rate means work is being done within your body. Your heart rate goes up and you breathe faster and both of these involve increasing the kinetic energy of some mass.
So, in the case of the barbell, even if someone else lifts it up and you merely put it back down your metabolic rate increases, work within your body is being done and the energy to do that work comes from your body and so you will get tired. You might last a while but I will get tired very quickly.
Well, by jumping up and down you are not doing any work on an external object but plenty of work is going on in your body, and you will get tired.
Plus the internal work done in the body to increase your heart rate, etc., etc.
Absolutely but that work doesn’t require any extra effort on your part. Your metabolism doesn’t increase so no extra work is being done in your body and so you don’t get tired, although I do if I stand too long. 
Right, but the work that is put into the machine because of your weight does not come from effort on your part and doesn’t tire you out. The only work that comes from your effort and tires you out is that work used to move your legs. The work that goes into the machine as a result of your effort is that extra impulse that is applied to lift your leg. That exerts a momentary downward force on the escalator and means that the motor doesn’t need to do as much work to maintain the speed.
The impulse results from the change in your body’s momentum as you raise your leg. The impulse is equal to the change in momentum and the force applied as part of the impulse depends upon how long the impulse lasts in time.
No, you can.
In any case, do you or do you not agree that your mere weight putting energy into the machine doesn’t result in any effort on your part since the evergy comes from gravity and not from you?
If so, then the only work that you do is a result of walking and that’s the same amount of work that is done in clumbing the stair. However, in climbing the stair you have to do extra work to lift your weight.
If you don’t agree that the work going into the machine because of your weight doesn’t come from your effort then we are back at the same old impasse and probably should move on to more useful enterprises.
The OP is concerned with how tired you get, yes. However, the OP was thinking that you would get less tired because you weren’t transferring energy to your surroundings (i.e., doing “physics work”). (From the OP: "The engineer in me is convinced that since they weren’t actually moving that they weren’t doing any work (W=F*D). ") So I was concentrating on this energy transfer. Of course, the OP can clarify, if he’s still interested.
I absolutely agree that work is going on inside your body, but I don’t know how to quantify that, and I’m not sure we even need to. I don’t sense that there’s much disagreement about what’s going on at a muscular level.
Yes, but look at energy flow. Your body is neither gaining nor losing potential energy. You can’t say that your potential energy is being transferred into the escalator (as in Case 3) unless some other form of energy is replacing it.
Mmm…I’m not sure where you’re headed with this. If you’re pushing on the stair with some force greater than your body weight (the “extra impulse”) then you’re accelerating yourself. If you’re accelerating yourself, then in thie time after the extra impulse, your force on the stair is less than it would be otherwise. I believe if you integrate the force over time, you’ll come up with a constant, whether you’re standing or walking or jumping. However, I think this is getting a bit far afield from the original question.
Sure.
So where does the work come from that prevents your weight from dropping when you walk on the escalator?
Here’s the crux of the matter: you’re overlooking the difference between Case 3 (standing on the escalator) and Case 4 (walking on the escalator). In Case 3 your body loses potential energy; in Case 4 it doesn’t. Energy can’t be created or destroyed, so what’s happening in Case 4 that isn’t in Case 3?
What’s happening is that your muscles are doing extra work, preventing your potential energy from decreasing. The same amount of work, incidentally, as they would do in Case 2 (walking up the stairs).
Wow! 114 posts on this. At least this proves that my question didn’t have a completely obvious answer. Thanks to everyone that participated, I have come to a conclusion based on your arguements. I’m not going to say where I stand on this now, because no matter which way I choose, it will add fuel to someone’s fire and this may never die.
::backing away slowly::
You’re either standing on the stairs or a moving escalator