I’ve read both sides of the argument on various forums, and one argument I’ve never seen made against those that say the wheels will spin but the plane won’t take off is this:

The question states that the treadmill will move in the opposite direction as the plane, not its wheels. If the plane is still, the treadmill won’t move at all.

Thanks for the links, but are you sure you understood my post?

Zhing: Let me see if I understand your question.
[ul][li]You say that there are those who argue that the wheels will spin but the airplane won’t take off.[/li][li]You say that the question states that the treadmill moves in the opposite direction of the airplane; not the rotation of the wheels.[/li][li]Therefore the treadmill will not move.[/ul][/li]Is that it?

That doesn’t really make sense because the assumption is that the forward movement of the aircraft is countered by the rearward movement of the treadmill. The whole point of the question is whether the rearward movement of the treadmill causes the aircraft to remain motionless.

Why doesn’t that make sense? If the plane doesn’t move forward, the treadmill doesn’t either.

This is what the scenario says:

It doesn’t say the treadmill will move in the opposite direction with equal speed as the wheels, it says the plane “moves in one direction, while the conveyor moves in the opposite direction”.

The way you’re phrasing that violates a condition of the scenario. If the plane is motionless, there is no rearward movement of the treadmill.

I think you’re picking nits.

And no, it doesn’t invalidate the scenario. The airplane is presumed to be stationary from an external frame of reference. If you were standing on the treadmill the airplane would be moving away from you.

I don’t think so; I’m merely following the scenario as described.

How do those that believe the plane won’t take off believe the conveyor will behave? Reading what they wrote, they believe the plane will stand still in relation to those on the ground but the conveyor will be moving. This breaks a condition of the premise:
“The plane moves in one direction, while the conveyer moves in the opposite direction.”
If they don’t believe the plane ever starts to move forward, then the conveyor can’t start moving backwards.

And the treadmill would be still (invalidating a premise).

No offense but I think you’re beating a spot on the ground where a dead horse died ages ago.

Because the premise makes no sense the way you are interpreting it.

Beating a dead horse implies that I or others have made my point many times over. Care to show me some examples?

Why not?

OK… The question assumes that at the instant (which has the properties of a ‘point’ – position, but no dimension) the airplane starts moving forward the conveyor moves backward. Thus, the airplane doesn’t actually move forward from an external frame of reference (i.e., someone standing on the ground to the side). However the airplane isn’t touching the treadmill. It rests on its wheels. The wheels turn.

Imagine a tank. Its tracks are like big metal conveyor belts. Now put the tank on the conveyor belt. The driver tries to move forward. The conveyor belt moves backward at the same speed. Now get this: The track actually touching the treadmill does not move in relation to the treadmill. But the tank moves in relation to the tracks. Imagine that you put a tape mark on the track near the front of the hull. Put another piece of tape on the treadmill right abeam the tape on the track. Now do the experiment. To an observer sitting on the tank the tape on the track and the tape on the treadmill will appear to move backward. Until the tank’s track turns up when it reaches the rear of the tank, and the treadmill turns down as it goes around the rear roller, the tape on the track and the tape on the treadmill will mot move relative to one another.

Now let’s say this is a very wide treadmill and you are standing on the treadmill right next to the tape mark at the front of the tank. When the driver tries to move the tank forward you see that the tape on the track and the tape on the treadmill do not move in relation to where you’re standing. But the tank appears to move forward. To someone standing on the tank, he thinks he is standing still and it appears to him that you are moving backward. To an outside observer the tank appears to be standing still and you appear to be moving backward.

Consider a wheel is like the tank track, only instead of having a long flat bit it’s circular. The part of the wheel that is in contact with the treadmill moves with it just as the tank track does. If you were standing on the treadmill the airplane would appear to move forward.

So the airplane does move forward – in relation to the treadmill.

Sorry, that doesn’t cut it. Show me exactly where. Ask Johnny L.A. how many times, if ever, anyone has brought up the point I have.

Hey, I’m just listing them; not committing them to memory!

Zhing, I hear you. The problem as it was originally proposed on these boards was stated in such a way as to making a straightforward answer impossible, IMHO. The key to this puzzle lies in the ‘treadmill matching the forward speed of the plane’ bit. The accepted answer here is that the plane’s forward motion operates independent of the wheels or the treadmill. So in the real world as soon as the throttle was hit the plane would just jet off of the treadmill. This was made possible by the introduction of “frictionless bearings” which were not part of the original question.

For any plane to take off, it must be moving forward in relationship to the surrounding air - something that was also not taken into consideration in the original puzzle. Obviously if a plane on a stationary treadmill is subject to a large enough headwind, the plane can just lift off without moving forward at all. But I think the question as posed here assumed a still environment. Given that, the plane must move forward in relationship the the ground the treadmill rests on. If the treadmill really can match the forward movement of the plane, the friction of the wheel bearings will prevent the plane from moving forward at all. So no taking off.

My thoughts are in the minority here.

Except that the prop is pushing against the air, not against the treadmill.

Maybe this link will help? There are opposing arguments (Q.E.D. at #36, **brewha **at #39) which explain why there is insufficient information to resolve the question.

You’re stating that “if the plane is still, the treadmill won’t move at all”. But, after the first couple of Newtons(?) of power are applied, the plane will attempt to start to move. It’s really that moment where things get interesting.

The gist of the question is this: If the plane is jet-powered, the actual thrust comes from those engines. They push against air. So, in a “perfect” scenario, the movement of the wheels doesn’t matter at all, because they don’t actually provide any push for the plane.

But in a real scenario, like brewha explains, there are all kind of considerations which we need to take into account to know whether the plane will lift off. So: which scenario are we talking about? What part of your scenario makes a significant difference from the “perfect” scenario?

Shouldn’t Johnny L.A.'s “thread collection” be a sticky by now?

Irrelevant. At rest the full weight of the plane is pushing down on the treadmill. As soon as the plane tries to move forward the treadmill will speed up sufficiently so that forward motion is stopped by the friction of the wheels.

If you put a real plane on a real treadmill (Mythbusters) the plane will take off. That’s because no real treadmill can speed up instantly to the fantastically high speeds needed to accomplish this - nor could the bearings hold up. But in the thought experiment first posed here the treadmill can instantaneously match the forward movement of the plane. Were that to happen, the plane could not take off as the drag would hold it back.

I disagree. As soon as the airplane tries to move forward, the treadmill will speed up to match the speed of the wheels. But the airplane isn’t connected to the treadmill except by a couple inches of rubber. There is no connection between the engine and the wheels. The wheels are unpowered. Since the propeller is moving the airplane through the air and not providing thrust against the treadmill, the aircraft will move forward and take off. The wheels will spin at twice the speed they would in a normal takeoff.