Final answer to the airplane on a long treadmill problem ...
The plane will fly and here is why...
Original problem:
There is treadmill and it is as long as a runway. The plane is sitting on the treadmill. The wheels on the plane are free-rolling. The treadmill will roll, in reverse, to match the exact speed of the plane. For example, if the plane is doing 100knots, then the treadmill will sping at 100knots in reverse. Will the plane take off?
Here is a simple experiment that I just thought up to try at home for those few left that do not believe...
Do this:
Take a matchbox car and put it on a piece of paper. Now, yank the piece of paper from under the car. Does the car move backwards? Not really if at all. What little bit is attributed to the friction in the wheel bearings.Now, imagine that the car had jet engines/packs on it and it was being pushed forward already via those engines. The paper still wouldn't do shit to stop the forward motion as the wheels roll freely.
Better yet, do this:
ROLL a matchbox car along the ground/table and when it gets over the paper (while it is still moving forward), yank the paper. Does it stop the car from going forward? I mean, you will yank the paper at a MUCH faster speed than the car is moving forward. Perhaps 10 to 20x faster. The car will STILL continue to move forward even though you yanked the paper (like a treadmill would do).
That is a real world example of why the plane would take off given a treadmill that was a long as a typical runway. [/discussion about this]
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