Conveyor Belt Question that does not involve Airplanes.

Factual Questions
81

[QUOTE=David Simmons]
We have no argument that if you do raise you CG by one rise with each step when on the escalator the two energies will be the same. I deny that your CG is raised. You can’t step on a tread, transfer your weight and straighten your leg instantly so as to raise your CG by the length of the riser when the tread is descending.

I am confident that you walk in place with very little change in the location of your CG by bending and straightening of your legs and gradual transfer of weight from one foot to the other and you do this regardless of where on the escalator you are.

This being our difference, it appears unresolvable by discussion. Off to the lab. :slight_smile:
[/QUOTE]
If you were suspended from cables like a marionette, then what you describe is right. But, in the OP’s scenario, you are standing on an escalator. Both you and the escalator are moving down relative to the store.

Here is yet another thought experiment. The earth is revolving at several hundred miles an hour west to east. Do you think that if you run west that fast you do no work?

82

[QUOTE=zut]
Again, yes and no. Force and energy is the same, yes. But work is also the same–the relative velocities and distances between you and the escalator are independent of reference frame.
[/QUOTE]
Irony.

Your position is not changing while going up the down escalator- you’re not doing any work. Saying “relative to the escalator” turns the escalator into a set of stairs within that frame of reference. Also, how does “relative to the escalator” impact the guy on the actual stairs? Now he’s having more work done on him! Sure, it’s a valid frame of reference, just not a very sensical one.

83

[QUOTE=1010011010]

Your position is not changing while going up the down escalator- you’re not doing any work.
[/QUOTE]

That doesn’t follow. You can do work without moving your center of mass.

84

[QUOTE=1010011010]
Irony.

Your position is not changing while going up the down escalator- you’re not doing any work. Saying “relative to the escalator” turns the escalator into a set of stairs within that frame of reference. Also, how does “relative to the escalator” impact the guy on the actual stairs? Now he’s having more work done on him! Sure, it’s a valid frame of reference, just not a very sensical one.
[/QUOTE]
It’s a perfectly sensible one. How about if we frame the question thusly: “How much work does a person need to do to climb a down escalator to remain stationary relative to the store”?

If a person climbing an escalator does no work to remain in place relative to the store, does he do less than no work if he stops climbing?

85

Imagine you’re sat on a chair (so you’re stationary, fixed frame of reference), and beneath you is a giant wheel with rungs at a stride’s arc length apart and the whole assembly is spring loaded with a tendancy to push against your legs (with, ooh, shall we say a force equal to your weight?). If you push the rungs with your feet alternately (turning the wheel in the opposite direction), you’d be doing work, right?

You’re creating a force with your legs against the rungs of the wheel to exceed the contact forces and move the rungs away from you (ie a distance moved in the direction of your applied force, therefore work done). Does anyone argue that in this hypothetical situation, because your CofG isn’t moving relative to the ground that no work is done?

Taken out of this silly fanciful giant wheel situation, I can’t see how the escalator is any different. The wheel’s spring force is replaced by 1/2m[sub]person[/sub]g, and the distance moved is the height of each step.

You move or not, you’re constantly applying a force equal to your own weight which is making something move relative to you (or you relative to it, it doesn’t matter, it’s all relative) and that’s work done. I think.

86

[QUOTE=treis]
That doesn’t follow. You can do work without moving your center of mass.
[/QUOTE]
If the mass isn’t moving no work is being done on it. You can expend a lot of energy and apply a lot of force to counteract other forces in the system and keep the mass from moving, but work isn’t being done on the mass by keeping it stationary.

If you want to look at it on a small enough level, every time your muscle fibers contract their individual molecules move, and thus, even when you’re pushing against a wall you’re still doing work… just not on the wall.

Work is done on him by the escalator once he stops applying the forces necessary to counteract the escalator. Less energy is used by the system, if that’s what you’re asking.

87

The best way to stay in one place on an excalator is to let it carry you one step, and then step back down.

88

[QUOTE=David Simmons]
The best way to stay in one place on an excalator is to let it carry you one step, and then step back down.
[/QUOTE]
Or press the Emergency Stop and just stand there.

89

[QUOTE=1010011010]
Irony.

Your position is not changing while going up the down escalator- you’re not doing any work. Saying “relative to the escalator” turns the escalator into a set of stairs within that frame of reference. Also, how does “relative to the escalator” impact the guy on the actual stairs? Now he’s having more work done on him! Sure, it’s a valid frame of reference, just not a very sensical one.
[/QUOTE]
What is ironic? You claimed that “from an external reference, you will do less work on the escalator.” Which isn’t true. I mentioned relative velocities only to explain why. Work is independent of the observer’s reference frame.

[QUOTE=1010011010]
Your position is not changing while going up the down escalator- you’re not doing any work.
[/quote]
That’s simply wrong. pretend my name is witty gave a perfect counter-example. Doing work doesn’t require an increase in the potential energy of your body. It just requires an energy flow.

[QUOTE=1010011010]
If the mass isn’t moving no work is being done on it. You can expend a lot of energy and apply a lot of force to counteract other forces in the system and keep the mass from moving, but work isn’t being done on the mass by keeping it stationary.
[/quote]
Yes, this is correct. However, you’ve recast the problem. The question isn’t “is any work being done on your body?” The question is “is any work being done?” You do work on the escalator.

90

[QUOTE=zut]
You do work on the escalator.
[/QUOTE]
Yes. Whenever you lift your leg to take a step you have raised your CG against gravity a tad and theerefore have done work. Work is also done in sliding the muscles over each other and this develops heat, raising your temperature and you sweat a little more. However, the work done in taking steps on the escalator is no different, and no more, that that done in taking steps on the stair. If you say that work is done on the elscalator then the same work is done on the stair.

The situation is that there is an impasse. Some claim that in walking up the down escalator you raise your CG which is then carried back down and so you have raised your CG on the escalator by the same amount as when walking up the stair for the same number of steps taken.

I claim that you might raise and lower your CG a little but it is by no means as much as when going up the stair. I don’t know about you guys, but I walk without bobbing my CG up and down and I’m sure I would walk the same way going up a down escalator.

There is not way to resolve this impasse by discussion. Tests must be made and no one is going to do that.

The OP must long ago walked off muttering to himself.

91

[QUOTE=David Simmons]
There is not way to resolve this impasse by discussion. Tests must be made and no one is going to do that.
[/QUOTE]
Please respond to this scenario:

92

[QUOTE=DanBlather]
Please respond to this scenario:
[/QUOTE]
The answer is obvious but what does that have to do with anything? Didn’t my previous post say that work is done in walking?

What are you talking about?

93

[QUOTE=David Simmons]
The answer is obvious but what does that have to do with anything? Didn’t my previous post say that work is done in walking?

What are you talking about?
[/QUOTE]
If you run at the same speed the earth is revolving then you are stationary to an outside observer. That is exactly the same scenario as being stationary on the escalator relative to an outside observer.

94

[QUOTE=DanBlather]
If you run at the same speed the earth is revolving then you are stationary to an outside observer. That is exactly the same scenario as being stationary on the escalator relative to an outside observer.
[/QUOTE]
Have you forgotten that we are comparing the work done in walking up a flight of stairs with the work done in walking in place going up on a down elevator?

Yes it takes work to walk in place on an escalator. It also takes the same amount of work to walk up s flight of stairs. For the umpteenth time, the question is whether or not the work done in lifting your CG is the same in both cases.

I’m not going to engage in any more such nonsense as your last few posts.

95

Make that “walking in place going up a down escalator.” not “elevator.”

96

[QUOTE=David Simmons]
Have you forgotten that we are comparing the work done in walking up a flight of stairs with the work done in walking in place going up on a down elevator?

Yes it takes work to walk in place on an escalator. It also takes the same amount of work to walk up a flight of stairs. For the umpteenth time, the question is whether or not the work done in lifting your CG is the same in both cases.
[/QUOTE]
Good god you are frustrating, you seem to have totally changed your position. You now seem to be saying that the same amount of work is done on the stairs and the escalator. But here you say what seems to be the opposite:

So what are you saying? Does the person walking up the escalator expend the same amount of energy as the person walking up the stairs? Is the amount of work the same in both cases?

97

[QUOTE=DanBlather]
Good god you are frustrating, you seem to have totally changed your position. You now seem to be saying that the same amount of work is done on the stairs and the escalator. But here you say what seems to be the opposite:
So what are you saying? Does the person walking up the escalator expend the same amount of energy as the person walking up the stairs? Is the amount of work the same in both cases?
[/QUOTE]
See, one way to analyze things is to separate out the various parts of the problem, go through them individually and then combine the results at the end to get the final answer. In fact the root of the word “analysis” is the Greek word meaning “to break up.” Let’s see if we can make this real, real simple.

Walking up a flight of stairs is a complex process consisting of two actions. One action is the simple act of walking. The other action is lifting your weight from one step to the next.

Let’s be careful now, mustn’t go too fast.

Now walking is walking so walking on the stairs is the same as walking on the sidewalk, or more to the point, on a down escalator.

Are you still with me?

It takes the same amount of energy (work), or very nearly the same, to do the simple act of walking regardless of where it is done. So the act of walking, taken as just walking and nothing else, up the flight of stairs takes the same energy (work) as walking, taken as just walking and nothing else, up a down escalator. We have now taken account of one of the actions, namely just plain walking all by itself.

Are we still tracking?

Next we take account of the weight lifting. When you ascend up a flight of stairs you lift your weight by about 9 ft. This requires additional work on your part over and above the amount of work done in just walking.

Got it?

So the total amount of work done walking up the stairs is the sum of the work in just walking and the work in lifting your weight 9 ft.

Now, on the escalator. One part of your action on the escalator is walking. The same walking as you do on the stair and all by itself it takes about the same energy as walking on the stair.

Now we need to take account of the lifting part, if there is any.

There is the claim that with each step you lift yourself the height of the riser but this work done is lost when the escalator brings you back down. By this reasoning the total lifting work done in this case on the escalator is the same as on the stair for the same number of steps.

Again the total work done is sum of the work done walking and the work done climbing. If this claim is true then the same amount of work is done climbing the stairs as is done when walking on the escalator and staying on average at the same level.

I claim the above is wrong. I claim that there is little lifting of your weight at all on the escalator because your CG never is raised very much in any step. Therefore I claim that the total work done on the escalator is approximately equal to the work done in just walking while the work done on the stairs is the sum of the walking work plus the lifting work.

Those claiming that you lift your weight on the escalator point to things like the Stairmaster exercise machine. I don’t think you necessarily lift your CG by the height of the step on that machine. When you lift your leg you have lifted a pretty heavy piece of meat to put it on the step above and if the machine is set so that you have to take rapid steps you get a damned good workout. Sure, when the step comes down the lifting work is returned but the process is very inefficient and a lot of the work done lifting your leg was lost in internal friction within the muscles of your leg. I’ve watched people on TV on the machine and they don’t climb up on the step and then ride down. The just stand in one place and walk while moving their body up and down hardly at all.

My posts are consistent. It’s just that in one post I’m writing about the walking part, in others about the lifting part, and in still others about both.

To sum up, walking is walking and the same energy for just that, or nearly so, is used both on the stair and on the escalator. However, i don’t think that you lift your body very much on the escalator.

98

Got it, that was perfectly clear. Now I need to find a way to convice you that the person on the escalator is indeed lifting himself up those 9 feet. The person on the escalator is in its intertal reference frame. Wikipedia says this:

The escalator and the person on it are in the same intertal reference frame. As such, there is no difference between the escalator standing still and the store moving up vs the escalator moving down and the store standing still. I assume that you would agree that a person climbing a stationary escalator is expending more energy than just walking. If the escalator is moving at constant speed and the person on the escalator is not connected to anything outside the escalator (i.e., suspended like a marionette or standing with one foot on the floor at the base of the escalator) then there is no way to tell the difference between the store moving or the escalator moving. Any measurements done will yield the same result.

I think this is best illustrated by the elevator scenario. A man steps on to a step stool while in an elevator. There is no difference among the elevator being motionless, the elevator descending at a constant speed, or the elevator ascending at a constant speed. All of these will look, feel, and be measured the same.

99

[QUOTE=DanBlather]
Got it, that was perfectly clear. Now I need to find a way to convice you that the person on the escalator is indeed lifting himself up those 9 feet. The person on the escalator is in its intertal reference frame. Wikipedia says this: The escalator and the person on it are in the same intertal reference frame. As such, there is no difference between the escalator standing still and the store moving up vs the escalator moving down and the store standing still. I assume that you would agree that a person climbing a stationary escalator is expending more energy than just walking. If the escalator is moving at constant speed and the person on the escalator is not connected to anything outside the escalator (i.e., suspended like a marionette or standing with one foot on the floor at the base of the escalator) then there is no way to tell the difference between the store moving or the escalator moving. Any measurements done will yield the same result.

I think this is best illustrated by the elevator scenario. A man steps on to a step stool while in an elevator. There is no difference among the elevator being motionless, the elevator descending at a constant speed, or the elevator ascending at a constant speed. All of these will look, feel, and be measured the same.
[/QUOTE]
There is a favored reference frame when you are computing the work that is done in opposing the gravitational field and that is the field itself. It is what considered as stationary while the escalator steps are going down. If you consider the escalator steps as stationary then the gravitational field must be moving.opposite the direction the steps were going with the field stationary. If the escalator is going down then the field is going up. In order to keep my weight the same I must ascend the escalator at the same rate theat the field is going up. On the other hand, the person going up the stairs is climbing into a slightly weaker field which means he must be climbing faster than I am. In order to climb faster doesn’t he need to exert more force and thus do more work?

100

[QUOTE=David Simmons]
There is a favored reference frame when you are computing the work that is done in opposing the gravitational field and that is the field itself. It is what considered as stationary while the escalator steps are going down. If you consider the escalator steps as stationary then the gravitational field must be moving.opposite the direction the steps were going with the field stationary. If the escalator is going down then the field is going up. In order to keep my weight the same I must ascend the escalator at the same rate theat the field is going up. On the other hand, the person going up the stairs is climbing into a slightly weaker field which means he must be climbing faster than I am. In order to climb faster doesn’t he need to exert more force and thus do more work?
[/QUOTE]
Change the underlined sentence to read "If the escalator was going down with the field considered stationary then the field must be going up when the escalator steps are considered stationary.

And maybe a little more is needed as to why the guy climbing stairs does more work. The gravitational field is always trying to pull you into a reagion of higher gravitation. The person on the escalator is climbing just fast enough to exert a force equal to his own weight opposing the pull of the field. In order to climb into a region of lowered gravitational field, the one going up the stairs must be exerting a greater force and thus doing more work.