Only because of the friction.
This is the right answer.
The toy car analogy is flawed. The wheels don't even have bearings. They don't spin freely at treadmill speeds.
Try the same thing with a skateboard or a good roller skate.
If you stop the skate from moving back with a gentle nudge of the hand it with remain stationary on the treadmill. This will overcome the initial friction that causes the skate to move.
Shoot a lubricated rocket over a conveyor belt moving in the opposite direction with arbitraty speed? You think the rocket is going to slow down? If yes, why?
Hence my rollerblade example.
The belt is NOT acting on the airplane. The wheels prevent that. If the landing gear got ripped off and the plane was laying on its belly on the ground, YOU WOULD HAVE A POINT.
If the landing gear got ripped off and the plane was laying on its belly on the ground, YOU WOULD HAVE A POINT.
Take has it right.
The backwards motion of the treadmill will exert a very slight backwards pull on the plane. The translation of this force is minimal, but it's still there. In this little theory world we're living in with giant plane-sized treadmills, the treadmill will have to move at a ridiculous speed, many times greater than that of the air speed of the plane, in order for it to exert enough force that the bearings are able to translate it to the plane itself to keep it stationary.
Lets say the thrust is one belt, moving right-to-left.
The plane is a ball, since we're concerned witht he wheels behavior.
The con belt is moving left-to-right.
If you spin the belts in the opposite direction, the ball stays in the same spot. Increase the speed of one belt, the ball moves relative to the belts. With me? If the belts are regulated to the same speed, the ball never moves, no matter how fast the belts spin.
The original question postulated that the con belt moves in direct response to the wheel speed of the plane.