HAY /sci/, logic problem!

There is a giant, 10 mile long stetch of runway with a 747 on the middle of it. The runway, however, is specially designed to move, much in the same way that a treadmill will move, in the opposite direction of the plane. Secondly, the treadmill is attached to a computer which will match the acceleration of the plane exactly and constantly, in the opposite direction.

What is the result of this experiment? Does the plane ever take off?

The computer matches the acceleration. F=MA, therefore the computer will turn the treadmill fast enough so the wheels of the aircraft provide enough resistance to resist the thrust of the jet engines.

The wheels will have to maintain enough acceleration to provide this resistance. It will spin faster and faster and this will result in the rubber of the tyres and axil of the wheels and the treadmill melting causing them to fall apart. Most likely the treamill will fall apart first.