Quote Originally Posted by Fast Shadow
I think the problem most people have (including me, initially) is that they imagine the plane would be able to take off from a very short treadmill, which isn't the case. The treadmill would need to be as long as a regular paved runway. But the thing I had the most trouble with is getting it through my head that the plane's engine drives it through the air, there is no power being delivered through the wheels. I'm such a car guy that it made that concept pretty tough to get ahold of at first.
I thought that I made that clear when I initially posted the question...

Suppose a plane is on a runway that acts as a conveyer belt. The conveyor belt is as long as a typical runway. The plane moves in one direction, while the conveyer moves in the opposite direction at the same speed as the plane. The wheels of the plane are free-rolling. Will the plane be able to take off?