Wow, it's like a 0.9r=1 thread I once had on another forum (1000 posts, 200 mine, with myself arguing against about 6 people who just didn't accept it does!).
bGIveNs33 said:
well of course there's no such thing as "zero" friction, but more or less that is the idea.
Actually there are certain liquids, such as Helium 4 which will becomes "super fluidic" when you cool them enough. They lose all friction!
Crazy stuff, but very interesting. They used to do a lecture course on it at my uni, but they aren't doing it this year, and I don't like fluid mechanics.
Clearly this "problem" the thread is about is a thought experiment because as soon as you start saying things like "Friction in the tires will cause the plane to slow down" you are being inconsistent, because you've already been assuming the conveyor belt can instantly and perfectly adjust it's speed to that of the plane, which is not going to happen in reality.
Given various idealised assumptions (no friction in the wheels, the belt can instantly and perfectly respond to the plane etc) then the plane will take off. The wheels are free to rotate as fast as they like.
I don't know if any of you have been to an airport which has a moving walkway (ie a conveyor belt). I think Atlanta has one, but it's been about 10 years since I was there. Heathrow certainly does. Imagine sitting on a shopping trolley on one of them, facing the wrong way, and holding a rope with your friend at the end of the belt is also holding.
You turn on the conveyor belt, and it pulls you away from your friend, the rope running through your hands. If you and your friend then gripe the rope, you stop moving, though the wheels of the trolley start turning as the conveyor belt moves underneath you.
If you and your friend then start pulling on the rope, you begin to move
against the flow of the conveyor belt, and get closer and closer. Since you are applying additional force to the rope, you can move against the flow of the conveyor belt. A similar principle works with this situation with the plane.