The thrust of the engines pushes the plane and axles the wheels are spinning on forward (as stated in the problem). Once the plane begins to move, then the treadmill turns on. The treadmill accounts for and this forward motion, speeds up, and causes the wheels to spin around the axle. The friction holding the still plane in one place is gravity, a downward force. Once the treadmill is going, the thrusters create a vector of force in the forward direction enough to overcome the downward force of gravity. The plane continues to move forward faster and faster and the treadmill/wheels continue to spin also, but again, only around the axle. Eventually the plane will gain enough forward speed to create lift under it's wings as it would on a stationary runway.

My initial response was no take off, until I tried to explain why, then I had to change it to damn, I think it will take off.

It doesn't say "wheel motion" - it says forward speed. No forward speed. Forward speed cancelled. No motion. No lift.

I'm confused. If the treadmill does not negate the forward motion of the plane caused by the jet engines, the entire question seems moot and pointless in its quest to be clever. If it DOES, as it seems the question meant to intend, then I agree with Flint.

But I'm not a scientist and I don't even play one on TV.

Sorry I'm late to this discussion, but I'm with Flint. The problem, as stated, does not allow for the plane to develop any velocity relative to the air. Only this relative velocity (wing vs. air) can give you lift. (All aeronautics engineers: No Lift Without Drag!)

Doesn't matter what happens "in real life," this statement
makes it moot.

Hey, that's what I said, Pie...and now I feel really intelligent because you ARE a scientist-type. :)

In fact, a plane that's stationary with respect to the runway can take off -- if there is a strong enough headwind. Don't believe me? Try holding on to a kite on a windy day.

No, it won't: Again: not "wheel motion" but forward speed. The specific scanario we are discussing involves a stationary plane.

Yes it can, because the question says it can, and does. That is what we are discussing:

Flint, the wheels are in contact with the runway. The wheels are spinning around the planes axle. The forward thrust of the plane moves the axle forward, while the wheels keep spinning around the now moving axle.

After thinking for a bit, it seems pretty clear to me that the plane will not move forward, and hence will not take off. I have written a cogent, well-argued, absolutely devastating post to explain to all you fucking idiots who think the plane will take off, that it will not.

As is my habit, I then reread the post and went about editing it to make it more organized, introduce additional supporting points, and just generally kick rhetorical ass. (Anybody who thinks my posts are incoherent should see my first drafts.)

In the process of doing so, I became convinced that the plane would indeed take off.

It's all about the wheels. What forces are at play here? We've got the engine pushing forward. We have the treadmill furiously spinning backward. Since this is physics word problem land, we don't have to worry about friction, and we're ignoring considerations of the plane changing speeds. It's true that the engines are pushing against the air, not the ground--but they're also pushing against the plane. The treadmill is also exerting a considerable force of identical magnitude in the opposite direction. However, this force has no purchase on the body of the plane. Because the wheels are spinning freely, none of the reverse force from the treadmill is applied to the plane.

I think we can all agree that we'd like to see it tried, preferably with a 747 or a Concorde.

Picture a bike on one of those moving things in the airport. If you stand off of the moving tread, and hold on to the bike while walking forward at the same speed the tread is moving backward, the bike will move forward. The wheels will now be spinning twice as fast, but the bike will be moving as fast in the opposite dirsction as the tread. In the plane example, the forward thrust of the engines = you holding onto the bike. The plane will move forward, ever faster.

Right steve!! because they are spinning around an axle.

The treadmill will have some backwards force, but not enough to prevent the plane from moving forward.

The treadmill is moving 140 mph backwards while the plane is moving 140 forwards. In order to prevent the plane from moving, the treadmill has to accelerate to the point where it produces more drag on the wheels and axles than the jet engines do. Not 140 MPH, more like 14000.

The stated scanario is that all forward motion is cancelled. As to "how" the treadmill does this, that's a different question.