Physics professor wrote:
1. The argument that the plane takes off is predicated upon the plane moving forward through the air.
2. For the plane to move forward through the air, it is necessary for the plane's wheels to be moving faster than the treadmill.
3. If the treadmill's speed matches the plane's wheels, the plane does not move forward through the air and the plane does not take off.
Show me where I am wrong.
Reading the discussion on the page i linked to above, I believe this is a correct answer. Points to consider:
1. In reality, the fact that there IS rolling friction between the wheels and the treadmill belt means that, lacking a force in the opposite direction, the treadmill would be able to move the plane backward. However, the frictional force to overcome is small in relation to the thrust an airplane's engines could produce (this process works the same regardless of whether the treadmill is running)
2. This means that if thrust equal to the force of the rolling resistance is applied, the airplane should be stationary while the belt and wheels move at equal speeds, but opposite directions. Any further increase in thrust should therefore lead to a positive acceleration force and the airplane should theoretically be able to take off eventually.
3. This scenario, however, as physics professor just wrote, means that the wheels will begin spinning at a faster rate than the treadmill belt, and thus may indeed violate the conditions of the problem, if it is interpreted to mean that the wheels cannot spin faster than the treadmill.
4. There also seems to be some consensus that in reality, if the treadmill were able to exactly match the speed of the wheels, both the belt and wheel speed would almost instantly accelerate to infinity, resulting in the disintegration of the wheels before the plane could take off anyway.