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so back to the original problem, any thrust created by the plane to move it forward is counteracted by the conveyor, therefore there is no forward motion, therefore the plane does not fly.
The thrust of the engines causes the wheel axles to move forward. This axle movement causes the wheels to spin.

The conveyor belt causes the wheels to spin about the axles.

The conveyor belt can not resist movement of the wheel axles. In order for the plane to NOT take off, the conveyor belt MUST prevent movement of the wheel axles. It can not, as the tires free-spin about the axles; they do not cause the axles themselves to move. The tires can ONLY push the axles IF they are powered at the wheel (like on a car). On a car, the axles move because the tires move. On an airplane, the tires move because the airplane moves. It's simple cause & effect... THINK ABOUT IT!!!

Therefore the plane will still accelerate as normal, and will take off upon reaching takeoff velocity.

There is nothing "flawed" about this logic. And I actually challenge any of the "can't fly" crowd to refute this post with proof. Good luck...

PS: You're going to need to prove that the conveyor belt CAN move the axles of an aircraft in order for your conclustion that it can't take off to be correct. There is no way the conveyor belt can move the axle as long as the tires are allowed to spin freely about the axle. None. No way. It's not physically possible. Not in theory, not in a lab, and not in the real world.

And once you realize the conveyor belt can not move the axles, then you *should* be able to realize that means the plane can take off, becaues the motion of the conveyor can not counteract the motion caused by the aircraft engines. Only 1 force in the example has any effect on the axles of the plane, and that's the engines of the plane. There is no counter-force to prevent the movement of the aircraft. The plane takes off.