I don’t understand the reasoning so far. Why is the surface of the ground the point to compare to rather than the surface of the escalator track on which you’re standing? If you mark a spot on the escalator track while this section is at the bottom, then watch it, you can see that the person is doing work to the extent that they are moving towards this mark on the escalator track. You should take the mark on the escalator as being the “stationary” point of reference because from the person’s perspective, it’s all that is.
Actually, I think I was wrong.
Oops, hit post too soon.
If you were in an elevator, lifting a weight from the elevator floor to waist height would require the same amount of energy regardless of whether the elevator is moving or not. (I assume it’s not accelerating). Viewed from the outside, it’s less work if the elevator is moving down, but it’d also mean more work for whatever mechanism is keeping the elevator moving in a constant motion. So walking up a down escalator is the same amount of work as walking up the stairs.
I think. 
Nooo!
I need support on this one. I’m taking the stance that walking up the escalator is the same as standing in one place doing knee raises.
For those who say that you are doing work because you’re exerting a force on the escalator and the stairs are moving, there is being work done on the escalator, but that work is done by the motor powering the escalator - not your legs. The stairs will move whether you are on them or not. The net force you exert on the stairs is the same as the force you would exert on a flat surface by standing still. You are not moving up or down, your potential energy is not changing, therefore, the force you exert on the stairs is exactly equal to the force exerted on you by gravity.
Yes, there is work being done, but it is not done by the person on the escalator.
brewha, let’s change it so that instead of an escalator, it’s the world spinning on its axis. If somebody were able to run so quickly that they were essentially staying in one spot while the earth rotated under them, would you say they are doing no work? That, just like this problem, depends on your frame of reference.
In the escalator/conveyor belt, the person is doing no work compared to a stationary observer off of the belt/escalator. In the spinning world example, to a person in outer space, the person is doing no work. To somebody on the escalator/conveyor belt/spinning world, the person is definitely doing work.
Is that any clearer?
Oops, sorry, I didn’t read your last post carefully enough.
In your case, yes, I think that the amount of energy used by the person to step up the escalator and a person staying on the ground doing knee lifts is pretty comparable. It’s not exactly the same since the motion is not identical, but it is pretty close.
Because there is displacement caused by force within this example, the answer is completely determined by the boundaries you draw in asking the question.
Even if you draw a boundary around the human and just consider the center of gravity when measuring displacement, you would still have up/down/left/right displacement with each step due to the imperfect nature of our bodies.
Seems like you have 3 options:
- Assume displacement measured by center of gravity and that imperfections in steps do not cause it to move, then no work relative to ground.
- Assume displacement measured by center of gravity but allow for imperfect stride, then yes work.
- Assume total work is the sum of all moving parts of the system, then yes work.
The not moving with respect to the ground is just a strawman.
The escalator is moving downward at a speed of X. The person on the escalator is moving upward and overcoming gravity. If the person’s speed upward is exactly X then with respect to the ground he is motionless. Work is still being done to achieve a speed of X.
If the person’s speed is < X but >0 they will still be doing work, but not as much, and at some point reach the bottom of the excalator.
If the person’s speed is > X they are doing more work, and will at some point get to the top of the escalator.
I completely agree with this post. As for #3, there is work being done, but most of it is done by the motor moving the escalator. The only work exerted by the person is the work to move their legs. There is no work required to move their mass.
Have any of you seen the Gazelle? Walking up an escalator without moving is similar to this. You are doing work to move your legs, but no work is done to move you.
My origional question (is staying stationary on a moving escalator less work than walking up stairs?) has been answered as far as I’m concerned.
I need for you to describe “doing knee raises,” brewha. In my previous response, I pictured lifting one leg at a time, lifting the thigh toward horizontal while the shin stays vertical, then lowering back to the original position. Now, I think you mean something different. Can you clear this up?
Yeah, that’s pretty much what I meant. Granted, it is not exactly the same motion as what you would do on an escalator, but it is close. My point is that the only work you would do is the work required to move your legs. No work would be done to move your center of mass.
Clearly (?) this isn’t the case. You’re lifting your body up the step in one case, while only setting down your leg in the other.
Sure, you’re stepping onto a step that’s coming down to meet you, but the step you’re ON is moving down, too, and at the same rate. The net effect is the same as if the stairs were stationary. In fact, in the reference frame of the escalator floor (and you) the stairs ARE stationary.
You are CLIMBING STAIRS. The fact that the whole system is moving relative to something else doesn’t change that.
Here’s a thought: compare climbing the stairs of a down-moving escalator to stepping onto the FIRST stair of that escalator. In this case, your action IS equivalent to a leg lift - the stair came down “with” your foot, and no lifting was involved. But that one step is the only case where this works, and it’s because you are still in the reference frame of the GROUND at that point - your body (at rest) is moving rapidly with respect to the escalator. Once you’re on it, your body (at rest) would NOT move with the escalator (and you’d be carried down by the escalator motor).
That last sentence should read “move with respect to” rather than “move with”
That’s my thinking as well. Or put another way, when climbing stairs, you are constantly moving your entire body mass upwards. Climbing an escalator, you are not. Then again, you are lifting your mass in discrete intervals, so maybe there is little to no difference.
The escalator motor is supplying enough energy to keep the escalator moving at a constant speed. When you’re walking up the down escalator, you’re supplying some of the energy needed to overcome the friction, and the escalator motor is working a little less hard.
Again, your legs are supplying a portion of the energy needed to keep the escalator moving, and the motor works a little less hard. With enough people all walking up the escalator, or with low enough friction, the motor wouldn’t have to work at all.
When doing leg lifts, you’re only applying enough force to lift your leg, maybe 20 percent of your mass. When you’re walking up the escalator, you’re applying enough force to support your entire mass.
Most of the work being done on the escalator is being done by the motor. When there’s nobody on the escalator, the motor has to do just enough work to overcome friction in the escalator bearings to keep the escalator moving at the same speed. When a person starts treading on the escalator, the same amount of work needs to be done to keep the escalator moving against friction, but now some of that work is being done by the person, and the motor does a little less work. Fundamentally, this ends up being the same sort of problem as the old classic with the car driving on the deck of an aircraft carrier.
Ah, very good point about the motor supplying less power. So, for my analogy, it’s not so much like standing on solid ground doing knee raises, it more like standing in quicksand doing knee raises and staying at the same height.
So, that throws a wrench in what I thought was a cut and dry case. I agree that walking up the down escalator is more work than standing in one place.
Is it still as much work as walking up stairs? It is now seeming more like it could be.
Hmm. I’m still thinking this is simpler than people are making it.
Let’s take a completely rigid staircase, and put it in an elevator.
Are we agreed that for any elevator speed short of freefall, that it still takes work/effort to climb the stairs, even if the elevator is descending? I’m willing to buy that you’re a LITTLE lighter on a descending elevator, but you’re not weightless.
If so, what’s the difference between that and an escalator?
Based on my elevator analogy, I don’t think it’s quite the same effort: your work is based on your weight, not your mass. Your weight will be very slightly less in a reference frame descending against gravity than in a fixed one. But it would be close for reasonable escalator speeds.
This would also imply that climbing a RISING elevator would take slightly MORE effort per stair than climbing a fixed stairclase, since you’re a touch heavier.
Consider a regular flight of stairs 100 steps high, each of height h. Next to it is an escalator of the same height, also 100 steps from top to bottom. One walker stands at the bottom of the stairs, and one stands on an escalator step. At the moment the rider is level with the stander, they both begin climbing at 1 step/second. After 100 seconds, the stairwalker hits the top step and stops. From his frame of reference, he has lifted his body weight 100(h) in 100 seconds.
From the rider’s point of view, he is on a stairway that is continually getting longer, with the top platform receding at some constant rate. Because the escalator is not accelerating, from the standpoint of the climbers it takes the same amount of energy to raise their body weights per step taken (mgh). The rider takes some longer period of time to reach the top platform; assume for the argument that he has to climb 120 steps in 120 seconds. From his point of view, he raised his body weight 120(h) in 120 seconds - he has done more total work than the stair climber.
It seems that there are two sources of confusion here: one, that a person on a downgoing escalator is ‘lighter’ because the escalator is moving downward. This would be true if the escalator was accelerating downward, but not if it is moving at a constant rate. The rider weighs as much as the stair climber, and has to push equally hard to lift himself from one step to the next.
The second source of confusion is the assumption that the amount of work done has to be the same from all reference frames. It doesn’t. From the rider’s point of view, he has climbed 120(h); from the stationary point of view he has only climbed 100(h).
On preview: you weigh the same in an elevator that is moving at a constant rate as you do when stationary. It is only when the rate of motion of the elevator is changing (ie starting and stopping) that your weight changes. As a descending elevator slows to a stop, you actually briefly weigh more, just as you will briefly weigh less as an ascending elevator slows to a stop. On an escalator, with constant motion, this does not apply.