Quote:
Which means John's point number 4 was incorrect, not number 3. That's what I was missing.

John's point number 3 was also incorrect.

Quote:
John's point number 3 was also incorrect. . . The plane must move relative to the air molecules in order to generate lift. . .

Quote:
So the question becomes what speed is the runway moving for the plane to move at all? Would it not become infinity? At that point, wouln't the wheel bearings be melted or frozen?

I just started thinking along these lines. It's interesting.

My first stab at it is this:

At takeoff, the conveyor belt would be moving at twice the speed of the airplane's standard takeoff speed. This would be fine, assuming the plane's tires can handle that much friction. I think the tires are probably rated for that.

I'm probably wrong, it's probably one of those things that requires the conveyor belt and the tires to reach infinity speed. I never understand those physics problems.

Quote:
Right, but if the airplane isn't moving and the molecules aren't moving, then the plane isn't moving

Quote:
once the engine starts thrusting, the belt would move backwards at the speed just enough for rolling friction of wheels to cancel the thrust

Quote:

Quote:
Which means John's point number 4 was incorrect, not number 3. That's what I was missing.

John's point number 3 was also incorrect.

Ok. I'll concede that. So the question becomes what speed is the runway moving for the plane to move at all? Would it not become infinity? At that point, wouln't the wheel bearings be melted or frozen?

Quote:
So the question becomes what speed is the runway moving for the plane to move at all?

Quote:
Would it not become infinity? At that point, wouln't the wheel bearings be melted or frozen?

OK, so the belt is allowed to go infinitely fast but the wheel bearings aren't allowed to be frictionless?

If the belt is perfectly frictionless and massless but the wheels aren't, then the wheels will burn out and the plane won't fly. If, on the other hand, the wheels are frictionless but the belt isn't, the plane will fly. If neither belt nor wheels is idealised -- if both are real-world objects -- then the answer depends on whether or not the wheels can survive the belt's maximum speed, i.e. on the engineering of the belt and the wheels.

I agree with JeffS, though, that this is probably not the physics question that the originator was trying to ask.

Peter

Quote:
I never said the airplane wasn't moving.

Quote:
3. Air will never move over the wings unless the plane makes forward progress on the runway.

Quote:
I just said the conveyor belt was irrelevant to the moving of the airplane because the plane's thrust doesn't act on the ground, it acts on the air.

Quote:

Quote:
once the engine starts thrusting, the belt would move backwards at the speed just enough for rolling friction of wheels to cancel the thrust

No: the friction doesn't increase with the speed of the belt. So either the thrust can overcome that fixed amount of friction (in which case the plane can take off from the belt, unless its wheels fail), or it can't (in which case the plane couldn't take off even on a normal stationary runway).

Quote:
However, since the runway and air molecules are relative to one another

Quote:
in order for the plane to move across the molecules it would have to also move across the runway.

Quote:
If the runway is a conveyor belt, it's moving independently of the air molecules.

Quote:
Depending on how you interpret the question, the runway is either moving the same direction of the plane's travel, or opposite the plane's travel, but either way, it's independent of the air.

The belt is moving OPPOSITE to normal wheel rotation. Says so upstairs there.
As the plane attempts to move forward down the belt the belt moves forward with it in order to cancel wheel rotation.
The plane is still moving forward down the runway and through the air, and past the control tower, the terminal, and the parking lots. Each increase in speed and attempt to turn the wheels forward yields an equal increase in speed of the magical belt.
At Vr the pilot pulls back on the stick and the plane takes off- giant treadmill or no. The only thing saved in the scenario is the tires and bearings on the plane.
End of story.
Honest.

The problem is supposed to help the students understand displaced reference frames.
Like running inside a box car in a moving train. You run 10mph relative to the box car, but relative to the ground you're doing You+Train.
In the example, the student has to dissociate themselves from standing on the belt watching for tire motion. Stand in the parking lot and everything is copacetic.

Quote:
Like running inside a box car in a moving train. You run 10mph relative to the box car, but relative to the ground you're doing You+Train.

Now assume that the train is travelling at the speed of light.

Quote:
That is, you're saying that relative to the plane, both the belt and air are stationary. But as viewed from a remote place, they could all be moving 200MPH.

Quote:

Quote:
Like running inside a box car in a moving train. You run 10mph relative to the box car, but relative to the ground you're doing You+Train.

Now assume that the train is travelling at the speed of light.

...through a dark tunnel...and then it turns on its headlights! Can you see anything?
What if you point a flashlight backwards down the path you've taken at lightspeed- are those photons 'moving' at zero velocity?

Quote:
Oh, and also, by the way:

http://www.avweb.com/news/columns/191034-1.html

Quote:
The question that has been going around is not particularly artfully worded, and I think that has caused some of the disagreements, but I'll repeat it as it is shown: "On a day with absolutely calm wind, a plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. The conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the airplane ever take off?"

Quote:
Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.
Can the plane take off?

The former suggests the belt moves opposite to the airplane's motion, the latter suggests the belt moves opposite to wheel rotation.
The bottom of the wheel (where it contacts the ground) is moving opposite to the plane's direction already.
Either way, though, and blah blah blah...

Quote:
Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyor belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.
Can the plane take off?