This is not a logic problem. This is a simple physics problem, once you understand the forces at work here (pun definately intended).

First of all, we need to conisider the problem… lets assume we’re talking about a Jet, though a plane with prop would yield the same results:

- Jet sits on a conveyer belt
- The conveyer belt will match the jet wheel speed at all times
- Will it fly?

Lets look at item #2… I drew a diagram.

Friction… friction occurs when there is slipping between two points. Lets look at the point where the wheel touches the conveyer. The point where the wheel touches the conveyer and the conveyer both have the same velocity and in the same direction. This means that there is no slipping between them, and thus, there are no friction forces that eminate from the wheel/conveyer interation.

http://www.mustangmods.com/data/18033/airplane.jpg

So, this illustrates that because the conveyer matches the speed of the plane’s wheels, there is no friction force eminating from the wheel/conveyer interaction.

This right here is the key to understanding this solution. Re-read if necessary.

If you’ve managed to understand the friction conclusion from above… we move on.

So now we look at what forces are left:

- Thrust force from the jet engines, T
- Gravity force (mass*g), N

When force T is applied to the plane, it will accelerate forward at a rate of accel = T/mass.

Now, here is where the understanding of friction forces from above come into play…

So, yes… when the plane accelerates forward, the conveyer accelerates also to match the wheel speed. BUT, since the wheel/conveyer interaction yields NO FORCES, there is nothing to counteract the “acceleration = T/mass” of the plane.

So, if the only acceleration is due to thrust, T, then the plane will move forward and take off.

http://www.mustangmods.com/data/18033/airplane2.jpg

We can ignore the Normal force due to gravity because that’s beyond the scope of the question.

So, in conclusion, the plane will take off