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#3
03-03-2006, 04:38 PM
 zut Charter Member Join Date: Apr 2000 Location: Detroit, MI Posts: 3,725
Welcome to the Straight Dope, Paradoxic. Your conclusion is certainly reasonable, but it depends quite a bit on the assumptions that you make about the situation. In fact, I listed a lot of those possible assumptions in this post relating to Cecil's earlier thread.

In particular, you are correct that, according to the original problem (at least, some versions of the original problem) the plane will be held stationary with respect to the ground, and thus the conveyor belt will apply the necessary force to counteract the thrust. And this force is, by definition, not inconsiderable. The real question that a lot of people asked was if it was even possible for the treadmill to apply such a force. Again, it depends on your assumptions.

However, a few things: First, mass is not an "inertial force." It's a component of the inertial force, but the force only occurs when the mass is accelerating (F=ma). Since we're assuming no motion of the plane at all, there's no inertial force associated with the bulk mass of the plane.

Second, assuming that the frictional force associated with the wheels will balance the engine thrust is problematical. Clearly, this frictional force is nowhere near the engine thrust when the plane takes off from a concrete runway. It's possible that the frictional force increases with increased velocity, but it would have to increase substantially, and this is by no means assured. A more significant force, I would argue, is the force resulting from the rotational acceleration of the wheels (as Cecil mentions).

Third, you are clearly correct that the airflow from the engines won't lift the plane, and that bulk flow over the wings is necessary. However, it is certainly possible that if the conveyor were long enough and ran fast enough for a long enough time, air could become entrained with the moving belt, moving fast enough to lift the plane off the belt.