
Originally Posted by samkim
Yes, but since the wheels of a plane spin freely, the treadmill wouldn't slow down the plane by much.
That's not true. The wheels of a plane may spin freely once the plane is in the air, but before that, they are subject to friction exactly like the tires of a car.
A knowledge of physics is a good thing, but without knowledge of the problem at hand, it can lead astray... As it said in the first post, "the treadmill has a clever design and always matches the speed of the plane, but runs in the opposite direction."
If that means the treadmill will always run at the speed the plane would have on normal ground, but into the opposite direction, the plane will not move relative to the air and not take off. I think this is clear and not disputed.
"Taking off" simply means "reaching takeoff speed" (about 275 km/h or 170 mph for an A320), meaning speed relative to the surrounding air. If we forget what the original question was and and just say "a plane stands on a treadmill which accelerates in some way until it reaches 275 km/h, while the plane accelerates into the opposite direction of the treadmill. Can the plane take off? Obviously it can, as long as it can go at least twice the 275 km/h and reach takeoff speed relative to the surrounding air. Relative to the treadmill, the plane would then roll at 550 km/h. However, in this example, the behaviour of the treadmill is different from the one in the original question (it just rolls at 275 km/h and does not continue to accelerate as the plane accelerates).
From this thought experiment, one can also see that the whole question has nothing to do with whether it is a car or an airplane. Think of a car standing on a treadmill going 50 mph. Can the car reach 50 mph relative to the ground/air around the treadmill? Obviously it can, as long as it is able to drive at a 100 mph in the opposite direction on the treadmill. The only difference is that 100 mph is not takeoff speed and the car doesn't have wings.
Both you and meyerweb seem to confuse the treadmill question with some sort of "zero friction" situation. With zero friction on the wheels, indeed a plane could move in the opposite direction of the treadmill, while a car could not (a plane gains thrust because it is pushed by the exhaust fumes in the jets, or pulled by the propeller, while the car needs the friction on the tires, which is zero in this example, so it cannot move).
However, in the original problem nobody ever said there is no friction, so all the talk about differences between a jet and wheels and planes and cars may be impressive, but irrelevant to the present case.


