Quote:
Originally Posted by cdcox
OK, now we are making progress. We've established that there are situations in which wheels and a treadmill cannot match speeds.
Back to the original airplane/treadmill case. There are two areas of slippage relative to the plane. The air slipping over the wings and the wheels and tread mill creating a similar plane of slippage between the plane ground. The jet engines are very powerful and are the driving force of the plane. After you account for the slippage of wind over the wing, they externally set the acceleration of the plane relative to the ground just as surely as the the tow rope sets the speed of the the person. You could speed the tread mill up, slow it down, run it backward, it would not affect the speed of the plane because the prime mover of the plane are the jet engines pushing against the air. The wheels will just free spin (slip) to compensate for the treadmill as needed to give whatever velocity needed to make the plane move at the correct velocity given the acceleration imparted by the force of the jet engines.
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If the wheels compensate speed at any point, the treadmill will do the exact same. Due to the structure of the question, the speed of the plane will
always be zero relative to the ground. Unless there is wind, there is no lift being created by the wings. 0 + X + (-X) + 0 = 0
If you want to want to discuss the problem in terms of force, the force counteracting the engine thrust comes from the wheel bearings. They would be spinning at an unbelievably unrealistic speed to generate that type of force, but that's why this question is theoretical. Therefore, the engines do not externally set the acceleration of the plane, as you must consider all forces acting on the plane.