The airplane on a treadmill

Question

An airplane stands on a huge treadmill. The treadmill is designed to run backwards at exactly the plane's forward speed, whatever that speed is. The plane starts its engines and tries to take off.

Can the plane take off? Explain what pushes the plane forward and what, if anything, the treadmill does to it.

Accepted Answer

Yes, the plane takes off almost normally. The treadmill just makes its wheels spin twice as fast. What moves the plane. An airplane is pushed forward by its engines, which push against the air, not the ground. The wheels are free-rolling; they carry the plane's weight and spin at whatever rate the ground beneath them demands. Nothing about the treadmill's motion is transmitted to the plane except a tiny amount of bearing friction in the wheels. What the treadmill does. As the engines accelerate the plane forward through the air, the treadmill runs backward at the same speed. So relative to th…

The airplane on a treadmill

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