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[Mainerunr]

Originally Posted by Zeek

Please stop saying the same thing over and over. The treadmill is going to increase in speed relative to the speed of the aircraft. Go out and buy a toy plane with wheels. Go to the gym and turn on a treadmill. While holding the plane, run it up the treadmill with the treadmill at 3mph. Next try it again at 5mph. Go ahead and try it at 10mph.

Now ask yourself, did your arm have to go faster to move the plane up the treadmill at the same rate while the treadmill was set at 10mph or 3mph? No? Well that's exaclty what will happen when the engines push the plane. The plane will move forward and the FREE SPINNING wheels will simply go faster. The engines don't have to work any harder.

read and comprehend what I'm saying then.

Originally Posted by CT_Nismo

If this Board were a bar I can envision drunken fisticuffs over an inane issue. The deciding point of this issue is not based in physics but legal interpretation.

First, we start with the problem statement:

"A plane is standing on a runway that can move (like a giant conveyor
belt). This conveyor has a control system that tracks the plane's
speed and tunes the speed of the conveyor to be exactly the same (but
in the opposite direction).

Will the plane be able to take off?"

The plane has speed so we can assume it's engines are on giving rise to the speed. "Tracking the plane's speed" implies that the plane's velocity is measured against a reference point not attached to the plane or the conveyor. Logically this would be the ground. The control system then commands the conveyor to move at the same speed but in the opposite direction to the plane.

When a plane takes off under normal conditions, (take off roll) the ground underneath the plane always moves at the same speed as the plane but in the opposite direction of the plane. This apparant motion is the same as the conveyor.

Therefore the conveyor does nothing more than a runway. The plane will take off.

thank you for quoting the exact question. worded that way, yes, it will take off. worded the way mountaineer was explaining it, no, it wouldnt take off.