You sound like you're itching to re-do the problem with accurate friction coefficients included!

The stated scenario is that the treadmill moves the same speed as the plane. According to your (flint's) take (faulty) on the question, the plane doesn't move and therefore the treadmill doesn't move.

Re-do whatever you want, but the answer to this question is: a stationary plane will not take off spontaneously.

No, the stated (post #1) take (this thread) is that the plane and the treadmill move at equal speeds, in the opposite direction.

Another way to look at it: can a sea plane take off if it's floating down a current faster than its takeoff speed? Sure, the minute its props spin, it will be generating enough force to overcome the friction of the moving water.

Just look at it the way is is, as stated.

You've got velocity and acceleration. The engines are applying force to the plane and therefore accelerating it. The treadmill has velocity, but it cannot impart any acceleration to the plane.

Here:

blah blah blah

The plane cannot move forward because the question tells you that. It doesn't matter "how" . . . READ THE QUESTION.

My bolding.

re-re-edit
 

butt

No labrat posts without going back to the butt! :)

Flint, I totally agree with you. The question says the motion is cancelled. No motion...doesn't matter how.

Ya, we know about your butt, okay. It's so awesome, etc.

If you read the red it in my quote as referring to the plane, then the answer would seem to be no, the plane can't take off. I read it as referring to the treadmill, thus the plane will take off.

The problem doesn't. It says the speed of the treadmill equals the speed of the airplane. It doesn't say the airplane is prevented from moving forward.

If the plane moves at a given speed in one direction, and the treadmill moves at that same speed in the opposite direction, what is the net speed of the plane? The debate is not: "how does the treadmill know what speed the plane is going?" it simply says the speed is matched, thus cancelled.

You're assuming that, in rotating, the treadmill exerts a backward force on the body of the plane. It's only interacting with the wheels.

Flint, when the treadmill moves, what part of the plane is it moving?

The wheels.

The wheels are free-spinning around their axles.

So, as the plane moves forward (which i thought you said it couldn't do ;)) the wheels end up spinning faster and faster as the treadmill matches the forward motion of the plane.

If the plane is moving forward at X mph, and the treadmill is moving backwards at X mph, then the net forward speed of the plane is X mph, but the wheels are spinning at 2X mph. The treadmill is matching the speed of the plane, not the speed that the wheels are turning.

another way to look at this is to consider the aircraft carrier: the planes are 'launched' with a catapult. But the wheels are on the deck, and the catapult moves much faster than the deck. The deck could be moving backwards and still the catapult could launch the plane.

Did my bike example make sense to you?

In order for the question not to contradict itself, you have to assume that the plane "moving forward" is only relative to the treadmill. It cannot "begin" to move forward, in any other sense, if the treadmill is moving backward at the same speed, as stated. What the wheels are doing doesn't matter. How the treadmill works doesn't matter. The stated scenario is that the plane cannot ever move forward because the treadmill moves backward at the same speed - not the same speed as the wheels, the same speed (realtive to the treadmill) as the whole plane.

No, I'm taking the question literally and establishing the parameters of discussion, to prevent going on irrelevant tangents.

Yes it makes perfect sense to me, as a description of a bike, a person, and a treadmill. We don't need "another" way. We need to read the question and not add anything to it.

Right. The treadmill is preventing the plane from moving forward because it matches it's forward speed.

Why does the treadmill moving backward prevent the plane from moving forward?

Because it matches its forward speed, as stated. X minus X is zero.

Nope. That is one interpretation, but that interpretation requires you to assume that planes don't work the way they do. It is not possible for the speed of a treadmill to affect the speed of the plane (short of mechanical failure in the wheels). Therefore, your interpretation is incorrect. You must assume that the plane is moving forward relative to the ground, and the treadmill is moving backward at the same speed, relative to the ground. That is the only physically possible interpretation.
Nope, the plane keeps going forward, the treadmill moves backward, and the wheels do double duty.

It doesn't have to, and I never said it did. Where did you get that? If the treadmill matches the forward speed of the plane, the plane cannot "begin" to move forward, except relative to the treadmill.

But the treadmill X can't subtract from the plane's X. The plane still goes X, but the wheels go 2X.

It can, because this question says it can. Start by establishing what is being discussed.

When you said that they could cancel each other out. That is not physically possible.The treadmill is moving backward relative to the ground at speed X. The plane is moving forward, relative to the ground, at speed X. The plane is moving at speed 2X relative to the treadmill. Your interpretation is not physically possible.

No, it doesn't. We interpret the question differently. Your interpretation is not physically possible, and mine is.

No. It doesn't. All it says is that the treadmill moves backward as fast as the plane moves forward.

Hope this comes through. Never thought I'd see such excitement about a physics problem! :D

That's a nice drawing, but the belt force arrow is in the wrong spot. It applies force to the surface of the weel's tire, not the axle.

All the excitement, in this thread, is regarding a semantics problem.

Which doesn't matter, because the question states what the result is, not "how" it works.

And the stated result is that the plane moves forward.

What? Is this the line you're having problems with?

Because it absolutely does not mean "...as the plane moves forward, the plane moves backwards beneath the aircraft", if that is what you're thinking. Context, man, context.

The question does NOT ask if the belt can move fast enough to keep the plane stationary.

It just says that the belt moves backwards at the same speed as the plane moves forwards. I interpret speed as the movement of something relative to a stationary object, namely the ground.

So if the plane is MOVING (key word folks) forward at 100mph, the belt is moving backwards at 100 miles an hour. The wheels are spinning as if the plane where traveling at 200 miles per hour.

In this interpretation, the plane takes off.

OK. If I change the original question to:
"A plane is standing on a runway that can move, like a giant treadmill. When the engines throttle up, the plane begins to move forward, but the treadmill runs at the same speed as the forward speed of the plane, only in the opposite direction. So, as the plane moves forward, the treadmill moves backwards beneath the aircraft.

As the engines throttle up, does the plane take off?"

What would your answer be?

:::stops reading::: I'm discussing the original question.Interpretation #1: The plane “begins to move forward” relative to the treadmill, “but” because the treadmill, by whatever mechanism (not stated) moves the same speed, in the opposite direction, the net forward speed of the plane is zero.

Interpretation #2: The plane “begins to move forward” relative to the ground, and the treadmill “match[es] the forward speed of the plane” (relative to the ground) and moves this speed in the opposite direction, causing the wheels to spin faster.
Can you (or anyone) please elaborate on the reasons why interpretation #1 is not “physically possible” ???

The plane is not moving ith respect to the AIR, the only substance that matters in this question. No air movement over the wings, no lift, no takeoff. QED.

And it doesn’t have to. It states “the treadmill is made to match the forward speed of the plane, only in the opposite direction” so, based on whether you are considering the speed of the plane to be relative to the surface it is on, or relative to the surface next to the surface it is on, you get either #1 the exact speed needed to keep the plane stationary or #2 a speed completely irrelevant to whether or not the plane is stationary.

This is a wind-up thread based on an unstated distinction which produces two different results.

Because the speed of the plane is not determined by its wheels. If you had a treadmill set up according to interpretation one, and the plane was being towed by a truck that was not on the treadmill, as soon as the truck started pulling, no matter how fast the treadmill went, the plane would be pulled forward, because the wheels would just move at the towing speed plus the treadmill speed. And then the magic treadmill would speed up to match that, and the wheels would speed up to match that, etc, etc, and it would rocket up to infinity.

The wheels are unpowered, so they will always spin at the speed of the treadmill (re ground) plus the speed of the plane (re ground). If you then set the speed of the treadmill to match the speed of the wheel rotation, you get a recursive equation. They can't both rely on each other.

Is it the word "but" that confuses? Drop the word "but" in the original question and replace it with the word "and". The conjunction does not change the meaning of the question.

Yes it is. The plane is moving with respect to the air at the speed that its engines propel it. The treadmill is irrelevant. The speed of the treadmill does not affect the forward motion of the plane relative to the air or the ground.

OK, let's try this one. The engine is not on at all. The plane is just sitting there. Now the treadmill/runway starts to turn, let's say at 10 MPH. What happens to the plane?

Friction or no friction?

It moves backwards because of friction. The important aspect here is that it takes very little force to overcome this friction because the wheels roll.

In Steve's scenario, the plane moves along with the runway if there is friction, and it stays stationary if there is no friction.

It's physics class so let's ignore friction. :angel:

It's the old pull-the-tablecloth-out-from-under-the-dishes trick.

Forget the wheels.

Wheel speed is not a factor in the original question, so you must assume that it is accounted for, or you are adding extra information. We need to leave the original question alone. But, if we did do what you said, I agree.
But it does, necessarily, affect the speed of the plane relative to the treadmill (see: Interpretation #1). Or, let's just stick to the original question, as stated.

Flint, you make about as much sense as Pie's diagram.

This scientific model is proof it works.

From the straight dope:
An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?
03-Feb-2006


--------------------------------------------------------------------------------

Dear Cecil:

Please, please, please settle this question. The discussion has been going on for ages, and any time someone mentions the words "airplane" or "conveyor belt" everyone starts right back up. Here's the original problem essentially as it was posed to us: "A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

There are some difficulties with the wording of the problem, specifically regarding how we define speed, but the spirit of the situation is clear. The solution is also clear to me (and many others), but a staunch group of unbelievers won't accept it. My conclusion is that the plane does take off. Planes, whether jet or propeller, work by pulling themselves through the air. The rotation of their tires results from this forward movement, and has no bearing on the behavior of a plane during takeoff. I claim the only difference between a regular plane and one on a conveyor belt is that the conveyor belt plane's wheels will spin twice as fast during takeoff. Please, Cecil, show us that it's not only theoretically possible (with frictionless wheels) but it's actually possible too. --Berj A. Doudian, via e-mail

Cecil replies:

Excuse me--did I hear somebody say Monty Hall?

On first encounter this question, which has been showing up all over the Net, seems inane because the answer seems so obvious. However, as with the infamous Monty-Hall-three-doors-and-one-prize-problem (see The Straight Dope: "On Let's Make a Deal" you pick Door #1, 02-Nov-1990), the obvious answer is wrong, and you, Berj, are right--the plane takes off normally, with no need to specify frictionless wheels or any other such foolishness. You're also right that the question is often worded badly, leading to confusion, arguments, etc. In short, we've got a topic screaming for the Straight Dope.

First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. But of course cars and planes don't work the same way. A car's wheels are its means of propulsion--they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane's wheels aren't motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane's wheels spin madly.

A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.

As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

--CECIL ADAMS

No, because wheel speed is identical to the speed of the plane relative to the treadmill. They are the same thing.
But the speed of the plane relative to the treadmill does not affect the speed of the plane relative to the ground. The plane's engine does. If the engine is going, then the plane moves forward relative to the ground.

My God I can't believe this problem generated 6 pages of posts.
THE PLANE TAKES OFF!!!!
Flint, you are saying we need to forget HOW a plane works and just assume that because of the word 'but' the plane cannot move forward, even though the question then goes on to say that all the treadmill is doing is matching its speed with the forward motion of the aircraft. Flint, you are correct if this was a car with wings, but because the speed of the ground has no effect on the speed of the AIR around the plane, it will take off normally.
Asking to forget everything about how the objects in question work and make an assumption based on a conjunction in one of the sentences is rediculous, there's no point to even making it a plane at that point then, we can't even assume the wings generate lift because the problem doesn't say that they do.

Flint knows the plane takes off from a "normal" runway treadmill. He's saying this is a special treadmill that somehow holds the plane back. He's deliberately looking for a way to misinterpret the meaning of the question just so he can argue. I don't know if it's face-saving on his part or just bullshitting on the internet. I assume it's the latter.

Pie, compare your diagram to mine in post 67. See the difference? This is critical. The treadmill does not move the axle, it moves the wheel around the axle. Thus, the planes forward thrust has no opposite force, and moves the plane (attached to the axle) forward until lift overcomes gravity and the plane takes off.

This has been fun, but I didn't get a damn thing done this afternoon. We need to add a NSFP* warning on these.

*Not Safe For Productivity.

Alright, mission accomplished! :thumbsup: