This is one of the most entertaining – and educational – online arguments I’ve had in a while. After a long night of online argument with people on both sides of the argument and a good night’s sleep, I think I’ve found the answer.
If you think the plane will stay motionless no matter how much the jet engines push, that is wrong. You’re thinking of a car’s movement, where the forward force comes from the wheels. In a car, since the conveyor belt always matches the speed of the wheels, the force from the conveyor belt negates the force generated by the car wheels. This is correct. However, a plane generates force from driving air through its jet engines, NOT from its wheels. Therefore the force generated by the conveyor belt does nothing to negate the force from the plane. There will always be a forward positive momentum.
HOWEVER – If you think the plane will lift off, unfortunately you are also wrong. You’re thinking of a constant-speed treadmill, or a freewheeling treadmill. In that scenario, you’re imagining that the conveyor belt imparts zero force onto the plane, so the plane receives force from the engines and can move forward on the treadmill. If this were a normal treadmill, you would be correct. However, the problem is that this is a magic treadmill that always matches the speed of the wheel. The plane can never have physical movement regardless of the net positive force applied to it by the jet engines, simply because the belt negates all movement.
This becomes an impossible scenario that breaks physics. On this magic treadmill, the jet engines will create forward thrust and indirectly speed up the wheel, but the treadmill will speed up at exactly the same time. The jet engine’s forward thrust forces the wheel to move faster than the treadmill, but the treadmill accelerates again to match the wheel. This speed-matching acceleration loop will spin the wheel to infinite rotational speed before forward movement can be achieved, despite the ever-present forward force applied by the jet engine. This breaks physics, because if there is a net positive force forward, an object should move forward, but the magic treadmill negates movement while allowing force, therefore breaking physics.
I suppose if we must have an answer, it would be this – The infinitely-accelerating wheels will eventually break and stop, therefore reducing conveyor speed to zero. The plane now has nothing to negate its movement, and can drag itself across the ground to move forward. However since I’m pretty sure the jet engines don’t have enough power to overcome the ground resistance from dragging its wheel-less body on the ground, the forward movement will not be fast enough to generate lift on its wings. It will move forward, but it will not take off.
This is one helluva riddle and is now my new personal favourite.