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Does the plane take off?

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A jet plane is on a long treadmill and the pilot attempts to take off in the normal fashion. The treadmill is designed to track the speed of the plane and go that exact speed in the opposite direction. Does the plane take off?

Now take the same situation and replace the jet plane with a propeller plane. Does the plane take off?

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Answer for a jet:

Yes.

Answer for a propeller plane:

Yes.

Reasoning:

An airplane takes off when its wings generate a lift force greater than its weight. Lift force is determined by air speed. A backward-running treadmill will not impede the plane's forward motion, nor limit its air speed, only make its wheels spin twice as fast!

But what if an airplane's engine drove its wheels? Then the answer would be No. It could not achieve forward motion nor generate lift.

That would be an interesting kind of airplane - after it took off it would become a glider!

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