Unless the plane is moving the same speed relative to the conveyor belt as the conveyor belt is moving relative to the ground, the plane is moving.
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Umm...it is being held in place - just like I get held in place by a treadmill.
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It doesn't matter what the episode says b/c these smart-guys already have it figured out...
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What you have to understand is that the plane will be moving ... there will be airflow around the wings. The wheels do not propel the plane at all, they are supposed to be as closed to frictionless as possible. All the conveyor does is spin the wheels, but that will not move the plane.
What moves the plane are the engines. The engines provide a net force forward. In an ideal world, there is NO force backward (edit: other than drag), even if the conveyor is moving 91832409832 mph backward, because the wheels are frictionless.
Therefore, the thrust forward by the engines propels the plane forward the same regardless of whether the plane is on stationary ground or a conveyor moving 2039840823904832098423094823094823094823 mph, and the plane can takeoff normally.
However, in the problem statement there is something incorrect. If the conveyor was truly moving the same speed as the radius of the wheels times the rotational velocity of the wheels in a no-slip condition, then the plane COULD NOT BE MOVING FORWARD. The thing is, this is only possible if the net force on the plane is zero. If there is any net force on the plane, the wheels will be moving faster or slower than the conveyor. THIS is what makes this problem so retarded.
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because the wheels are frictionless.
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the plane uses its engines to combust the air and force it backwards