Originally Posted by
Chainsaw_Willie
Realistically it can't. That's the problem with the conveyer speed = wheel speed argument, or the beauty of it depending on your point of view.
There are two different problems that have gotten tangled up in this thread.
The original question, way back when, involved conveyer speed = plane speed. In that case the plane clearly takes off and the wheels will be spinning at twice the plane's and conveyer's speed when it does.
The second question is more problematic because a condition was stated in it that can only come true if the plane doesn't move relative to the ground. That condition is that conveyer speed = wheel speed. As long as that MUST be true, the plane cannot take off because it won't move.
It's not that it's not physically able to move, it's not that you couldn't crank up the engines and make it move, it's not that the conveyer is somehow preventing it from moving, it's that you are working within the constraints posed by the question, that the wheel speed MUST match the conveyer speed. The only way that can happen is if the plane doesn't move, and if the plane is not moving it can't take off unless you find another way to create enough airflow over the wings to provide lift (the fan).
I've already answered how preventing the plane from moving can be accomplished, either by anchoring the plane to the ground somehow, or using the plane's engines to perfectly match the rolling resistance of the wheels.