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If the purpose of the conveyor belt is cause the plane from thrusting forward (independent of the wheels or friction or whatever)--in other words, if the backward speed of the conveyor belt is inversely proportionate to the forward thrust of the plane--I don't think the plane would take off.

But the forward thrust is a force, and the backward speed of the conveyor is a speed -- they can't be directly compared.

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Ultra-simplified example:
Airplane’s forward speed (500 mph) - conveyor belt’s inverse speed (500 mph) = the plane is essentially stationary.

The plane's engines don't cause "speed" directly, they cause force. Like Newton said, force is mass times acceleration. The forces acting on the plane are thrust (forwards), friction (backwards), weight (downwards), and lift (upwards). If the forwards thrust exceeds the friction, the net forwards force is nonzero and so the acceleration is also nonzero. The plane moves relative to the rest of the airport, and so also relative to the belt. The belt simply can't apply enough force to the plane to counteract the forwards force of the engines, especially as the effective friction force on the plane does not increase with the speed of the belt. As the plane speeds up, the lift also increases until it exceeds the weight, at which point the net vertical force is upwards and the plane takes off.

Peter