I saw this puzzle while browsing around the net this morning, and the comment threads that usually ensued were absolutely fascinating, so I thought I'd see how the dkos community would react.
I'm posting this as a diary because I want to include a poll. Take the poll, and if you'd like, explain your answer in the comments. I'll post my answer in an hour or so.
The puzzle has popped up in many places, but I'm copying from here:
Will a plane on a treadmill take off?
OK, I have seen this question posted on a couple other message boards I go to, but seeing asd most of the people at those messageboards don't have a large knowledge of physics, I am posting here in hopes to get the correct answer.
Imagine a plane is sitting on a massive conveyor belt, 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.
Can the plane take off?
I say no, because the plane will not move relative the the ground and air, and thus, very little airflow will occur over the wings (the engines will create a small amount, but not enough.) However, other peopel are convinced that since the wheels of a plane are free spinning, and not powered by the engines, and the engines provide thrust against the air, that somehow that makes a difference and air will flow over the wing.
So what's the real answer here?
OK, here's my answer:
The plane does take off. The key point to remember is that airplane wheels are not driven, but instead rotate freely. Thus, the treadmill can do whatever it wants to the rotation of the wheels, but no net force (or very small net force due to friction) is exerted on the plane. The engines thrust as usual, the plane accelerates as usual, and if you go through the math, the wheels spin at exactly double their normal speed. Assuming that the bearings and tires can take that higher speed, the plane takes off as usual (or possibly slightly longer takeoff run due to some friction effects).
A car, which accelerates by powering its wheels, would be stationary under this scenario, but an airplane's engine is a reaction drive (like a rocket) and doesn't care what the wheels are doing.
-dms