Conveyor Belt Question that does not involve Airplanes.

Factual Questions
1

If you walk on a conveyor belt and stay motionless WRT to the ground, do you do any work? I was watching “The Biggest Loser” last night and the final challenge was for them to stay on an moving escalator as long as they could. It was apparent that they were doing some kind of work as they were all sweating profusely by the end of it, but I was wondering if was as difficult to stay on an escalator as it would be to walk up stairs.

The engineer in me is convinced that since they weren’t actually moving that they weren’t doing any work (W=F*D). Was what they were doing any harder than standing in one place doing knee raises?

Of course, this is complicated by the fact that treadmilling is exercise. No movement, but it is still a workout. If you were using a non-motorized treadmill, I could see that you could say that you are moving WRT to the conveyor belt. But, on a motorized treadmill, the motor is doing the work to move the belt and you are just keeping up. If you were wearing rollerskates and holding on to the handrails, the only force you would exert would be to counteract the friction of the wheels and to counteract the normal force due to gravity(the same as if you were just standing still).

If you are running on a treadmill, I could see that the workout you are getting is from you effectively jumping from one foot to the other. The work would be the force required to move a small distance up, then gravity pulling you down - repeat as neccesary. Walking on the treadmill would be equivalent to simple shifting weight from one leg to the other(maybe moving your legs abit) without actually doing any work.

Does my question make sense? Can someone explain to me why staying on an escalator is actually work aside from just counteracting friction?

2

You are moving, though. The exerciser is in a moving reference frame (the treadmill or escalator), and relative to that, the exerciser needs to keep doing work to keep moving (in the same speed and opposite direction that the treadmill itself is moving).

It’s only with respect to the outside observer’s reference frame that the exerciser seems to be still.

3

What about the escalator scenario? To climb a flight of stairs, you fight gravity all the way to the top. On an escalator, you are not moving horizontally or vertically. No, change in potential energy occurs.

What my question boils down to is: Is it harder to walk up a flight of stairs or to stay on a moving escalator?

Timewinder, I see your point and I’ve already considered that. Logically, it makes sense, but I’m trying explain it to myself as a sum of forces type of problem. Can I say that the work that is done is equal to the work done by the escalator motor, but in the opposite direction?

4

On the escalator, you are fighting gravity. As you step up, you are supporting your weight on one foot instead of two so that takes effort and you are also usually stepping up faster than the tread moves down. There is no net gain in elevation due to hesitations between steps. If you stepped at exactly the same rate as the tread moved down, then you would essentially be marching in place, which is an excellent cardiovascular workout as it takes energy to lift the weight of your leg against gravity.

5

You have done NO WORK, the escalator has done the work to raise your position aka potential energy. You ARE moving both horizontally and vertically.

Surely you jest! Pull the other one, it has bells on it!

Do not confuse the work done by yourself with the work done by the escalator in moving you from on elevation to another.

6

**spingears **

I don’t know if you understand my question. When I say stay on a moving escalator, I mean that the escalator is going down and you are walking up at the same speed. You are not moving horizontally or vertically with respect to the earth.

Sorry if this was unclear.

7

I’m presuming they are walking up a down elevator, so that they are staying at the same height. (On preview, what brewha just said.)

Work = Force * distance. With each step, they are applying force to the elevator with their feet, and it is moving, so they are doing work.

8

I guess maybe this is more of a debate than a question.

If the force applied to the escalator by your feet caused the escalator to move, I could see that you are doing work. But, if you are standing at the base of the escalator, it is already moving and you are not (WRT ground). When you start climbing the escalator at the same speed as the escalator is moving, once again, the escalator is moving and you are not ( WRT ground).

It doesn’t make sense to me how standing in front of an escalator is less work than standing on it and keeping up. Logically I can see that it is, but is it any harder than standing in one place and doing knee raises?

9

The answer depends on if you are asking a physics professor or a physician. If work is a function of distance, then no. If work is a function of cardio-vascular exercise, then yes.

I would say, however, that walking up stairs is harder than walking up a down escalator. In the latter case, the stairs are moving down as you climb, making the climb a bit easier.

10

If you are standing in front of the escalator, you are applying force to the ground, but the ground isn’t moving, so you are doing no work.

When you are walking up the down escalator, you are applying the same force, but the steps are moving down, so you are doing work to the escalator. This work is coming from your muscles.

If you are standing on the escalator, and moving up, the escalator applying force to your feet, and doing work to move you up.

If you are standing on the elevator moving down, you are applying force to the escalator, and doing work to push the escalator down (the energy for that comes from your potential energy, not from your muscles).

tdn, I can think of no reason that walking up stairs is harder than walking up a down escalator. I believe you’re mistaken on that point.

11

That’s correct. You aren’t doing actual work in the physics sense, but you are expending energy to make up for wasted energy caused by the up-down movement.

Actually, running on a flat road is almost the same. You aren’t doing work when you’re running at a constant speed. You’re just expending energy to make up for the inefficiencies. (You do have air resistance to overcome, but that’s pretty small at jogging speed.)

Simply, there’s more wasteful up-down movement on the escalator. If you’re walking so smoothly that your center of mass doesn’t move at all, it should be as easy as walking on a treadmill. But most people won’t walk on an escalator like that; they’d take a quick step up (which takes energy), then let the escalator carry you down a few inches while you raise the other leg to the next step.

12

I’m not buying this “not doing work” argument. The distance wouldn’t be relative to the earth, but to the conveyor belt/escalator. If you mark a point on the belt/stair, and then proceed to turn it on and start walking, that spot will travel away from you. Hence, distance.

13

For once, the fact that I’m not an engineer or a physicist is a slight advantage, because I have no choice but to explain in layman’s plain language. The fact that The Walker is not moving relative to the earth doesn’t mean he isn’t doing any work. Compare it to a hovering hummingbird; the bird isn’t moving, but it’s resisting gravity’s pull on its body.

Now, the comparison to doing knee raises: On the leg’s upstroke, it is lifting only the leg’s own weight. On the downstroke, though, you have to add gravity’s pull on The Walker’s whole body weight, including the other leg.

Now, the first question: The motion of the escalator does reduce the amount of work done (relative to climbing stairs for the same amount of time.) Why? Because the machine assists The Walker’s downstroke by moving away. Regular stairs won’t give you that help.

I can’t give you formulas for any of this. I’m not trained for that.

14

If you are doing work, where does the energy go? When you’re climbing a stairway, it goes into the potential energy (your body ends up at a higher place). When walking up a down escalator, there’s no place for the energy to go, except for frictional losses (which you also have when waking up the stairs).

15

No, it would be as much work as walking up stairs.

It goes into the friction of the escalator’s motion. The stairs are not moving.

16

In physics terms, you are doing work running on a flat surface. You must exert a force to move forward, and you move forward some distance, and F x D is what work is. When you plant a foot, your leg absorbs some energy and you slow down. That leg has to push you forward to re-accelerate. (I think high-performance runners learn to keep their speed through a stride nearly constant, as well as the height of their center of gravity. Casual joggers just plod along one step at a time.)

(Now standing still, pushing on a wall as hard as you can, will expend energy and supply a force, but distance is zero so there is no work.)

I agree with the viewpoint that you are doing work relative to the treadmill, although it’s less work than running on the flat, because you don’t have to propel your center of mass forward, accelerating to overcome inertia with each step, as in road running.

17

And this friction loss just happens to be equal to mhg? Why?
(m: mass, h: vertical distance travelled, g: gravitational acceleration.)

18

RE: walking up the down escalator: You are doing work to move up the escalator, and the escalator is doing an equal and opposite amount of work to move downward. Hence you appear to not move. But work is being performed.

19

Actually, I think the answer is even more basic then those already posted.

Let’s use a time interval of X, which is equal to the time it takes the escalator to move the step down 1 position. (ie if you took a snap shot, the stairs would look the same, but each individual step would be one lower then the previous photo)

h is the difference in height between to adjacent steps
d is the width of a stair.
Starting location is height =0, horizontal location=0

So in 1 time interval (x) a penny placed on a stair would move down h and forward d.

So the penny isn’t doing any work, and it’s moving with the escalator.
Time0, location=0, height=0
time 1, location=d, height=-h
time 2, location=2d, height=-2h
etc

Now put a penny and a person on the same stair, with the person climbing up.

Time0, Penny location=0, penny height=0, person location=0, person height=0
time 1, penny location=d, penny height=-h, person location=0, person heigh=0
time 2, penny location=2d, penny height=-2h, person location=0, person height=0

The work that is being done may look, from the outside, like nothing, but that’s only if you don’t take into account the work that the escalator is doing in the opposite direction.

The work done climbing in place on an escalator should be the same as the work being done climbing stationary stair. It’s just that there is offsetting and opposite work being done by the escalator.

20

On second thought, can we just go back to arguing about the airplane? :smack: