<p>Just so everybody understands, here’s a little of the physics of what would actually happen with this (assuming the tires/wheels don’t fly apart), if we also let the thrust of the plane go to infinity.
In the ideal case, we just say that frictional force is mu*N, N the normal force. If that’s the case, then the velocity of the treadmill wouldn’t be able to stop the thrust, since mu cannot be higher than 1. In this case, what I said would still hold because of the inertia in the wheels due to the ridiculous acceleration of the treadmill. But note this (Source: <a href=“Force”>Force)</p>
<p>Part of the standard model of surface friction is the assumption that the frictional resistance force between two surfaces is independent of the velocity of relative movement. While this is approximately true for a wide range of low speeds, as the speed increases and air friction is encountered, it is found that the friction not only depends on the speed, but upon the square and sometimes higher powers of the speed. If there are fluid lubricants involved, then viscous resistance is encountered, and it is speed dependent.</p>
<p>Frictional force just models interatomic forces, so it’s understandably a bit odd.</p>
<p>Very quickly the converor belt will be moving at impossible speeds, but this is a hypothetical question, and it is indeed able to stop the plane while moving at a finite speed as long as the plane’s speed is finite.</p>
<p>Now, if we don’t assume a perfect world, then there’s another interesting thing that might happen (aside from tires blowing out).
Very quickly after the aircraft attempts to move forward, the conveyor belt is spinning under the aircraft at thousands of feet per second. Friction between the air at the surface of the converor belt and the belt will cause the air to move with respect to the ground next to the belt. At some point the magic belt will be moving fast enough to generate enough airflow over the wings that the aircraft will lift off the belt, again assuming the belt and wheels/tires are magic and do not fly apart. So, yes the aircraft will lift off the belt. What happens next is the subject of another debate.</p>
<p>In fact, I am finding this version of the problem rather more interesting.</p>