So, did anybody prove any physical laws wrong yet?

ATLidiot? I see that one's still trying.

I think the thing that most people who say the plane will not fly are missing is that there are two independent systems of force and resistance here BOTH of which affect the wheels. The thrust and forward movement affect the wheels through the spindle via the airframe; the conveyor affects the tires directly through frictional contact.

The first system of force/resistance is that of the aircraft's engines upon the atmosphere surrounding it. The engines create a low pressure area in front of the plane and a high pressure area in behind the plane. The difference in these pressures is what drives the plane forward and it will do this unless some other force prevents it. The wheels and wheelbearings (rolling resistance) here are an extremely small part of the resistance to this force. The main resistance to this force is the mass (not weight) of the aircraft itself and also wind resistance against the airframe of the aircraft, which increases as the speed of the aircraft increases. So long as the engines produce enough thrust to overcome these forces, the airplane will move forward.

The second system of force/resistance is that of the conveyor and the rolling resistance of the wheels. The conveyor acts upon the wheels with very little force, as not much force is needed to overcome the rolling resistance of the wheels and the wheelbearings. Because the wheels are not glued, nor are the brakes of the aircraft on the tires simply roll along the conveyor belt, making up for the speed difference between the aircraft and the conveyor belt; just as they would if it were a normal take off. The only difference is because the conveyor belt is moving in the opposite direction of the aircraft, the wheels are spinning twice as fast as normal.

Only when one incorrectly tries to combine the two force problems into one force problem does it appear the airplane does not move. A simple conveyor belt acting on the aircraft's wheels CAN NOT significantly affect the airspeed of the airplane. Some other force would be needed to counteract the thrust of the engines.

Saying that one force/resistance problem directly and significantly affects the other force problem is like saying the air conditioning unit in a sky scraper must be able to overcome the winds outside the sky scraper. The two are separate force/resistance systems with the only common link being the building; just as with the airplane, the only common link is the wheels. Both force/resistance problems directly affect the wheels, but neither force/resistance problem directly affects the other. Both act on the wheels which is why the wheels need to spin twice as fast as normal; one force acts to spin the wheels X amount and the other force also acts to spin the wheels X amount so the resulting WHEEL speed = X + X while the AIRSPEED of the aircraft and the speed of the conveyor belt both = X.

The conveyor does have a very minor effect against the thrust of the aircraft's engines, but this is limited to the the amount of force that can be applied through the rolling resistance of the aircraft. However, the conveyor would less of a chance of "holding back" the aircraft through this resistance than a Kia Spectra clutch (rated @ 100-something ft/lbs) would of holding the power of a top fuel dragster (in excess of 8000 ft/lbs).

Also, remember the problem states that the conveyor matches the speed of the aircraft and NOT the wheelspeed of the aircraft. If the conveyor DID attempt to match the wheelspeed, it would never be able to do so and both wheel-speed and conveyor-speed will accellerate at an exponential rate, yet the aircraft WILL move forward; that is until the tires disintegrate a few seconds into the run (so in that instance, the airplane would crash & burn rather than take off) However if we had tires, wheels and wheelbearings capable of an infinite wheelspeed at or near zero rolling resistance, then the aircraft would STILL take off and the wheels would simply be spinning incredibly fast as would the conveyor belt.

Also, I've given thought about this and changing the scenario to a normal wheel driven automobile and the common thinking that the car would remain motionless. This is only true if the speed of the conveyor is dictated by the wheelspeed. However, I don't believe that is the case from the original wording. It would appear that some device is used to determine the vehicles actual speed relative to the ground (a speed-radar perhaps).

If this is the case, then indeed the car would accellerate. The speedometer of the car would read twice the actual speed, but the car would be moving forward. In fact if the gearing of the car were changed to be 1/2 of what it is normally (e.g. 2.05 gears instead of 4.10's), the car would accellerate approximately at the same rate as normal (there would be some additional power loss incurred as a result of needing to spin the wheels 2x as fast as normal). Never the less the acceleration of the vehicle would be relatively unchanged, even without a gear swap, the only thing the motion of the conveyor would do is limit the top-speed of the car as the car would simply "run out of gear" (or at least any car with a decent amount of power would).