Letters to the Editor
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The treadmill can match the tire speed
"The speed of the treadmill will always be less than the speed of the wheels. It cannot catch up. Every time it spins faster to match the speed of the wheels, it spins the wheels faster. The wheels will always be spinning at the speed of the treadmill plus the speed of the plane."
Why? The question specifically states that the treadmill is designed to always match the speed of the wheels. If the plane accelerates down the treadmill runway due to engine thrust, the treadmill will speed up to match the speed of the wheels.
I believe the whole point of this question is simply to demonstrate that planes get no thrust from the wheels and all the thurst comes from the engines. You could get rid of the cumbersome treadmill and imagine the plance on a runway coated with perfectly smooth ice. Could it take off? Yes it could (if we ignore the problem of steering straight down the runway with no traction)All the tires do is support the plane until lift exceeds the force of gravity and the planes becomes airborne. How did it get so complicated?

