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Originally Posted by LabRat
Pie, compare your diagram to mine in post 67. See the difference? This is critical. The treadmill does not move the axle, it moves the wheel around the axle. Thus, the planes forward thrust has no opposite force, and moves the plane (attached to the axle) forward until lift overcomes gravity and the plane takes off.
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Okay, this is the absolute last post I'm going to make on this subject. (promise!) If the wheel experiences a force, that force
must be transmitted to the axle. (The other alternative is that the wheel goes that-a-way while the rest of the plane stays put.) The free body diagram holds.
The straight dope misses this point:
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A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.
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That "pull yourself forward easily" is impossible. To move yourself forward at all (even a micron per hour) still necessitates a net imbalance in the forces acting on the axle of the wheel; this is patently impossible, given the wording of the problem. F1 == F2
by the very statement of the scenario, so no net motion.
Newton would be scratching his head.