We don't need a mathmetician, we need someone who has a solid understanding of Newtonian physics (also called classical physics).

This is a basic question of force. Will the plane attain the force required to overcome gravity? As I stated it will.

The conveyor belt will not translate enough force to hold the plane in place. If the wheels are moving freely (indicating low friction) the force translated to the plane (through the landing gear into the main structure of the plane) will be very low. The thrust force generated is very high. The plane moves forward, the belt speeds up.

The plane will continue to gain acceleration and therefore velocity needed to attain a lift force from the wings (as stated by someone else before - it is actually the pressure differential between sides of the wing that cause lift). The conveyor belt will speed up, and will transfer more force to the plane; however, this force will be very small, and as already stated not enough to overcome the thrust). At this point the belt would be moving very fast, however the plane would continue forward relative to it's starting point. The plane will therfore reach an airspeed suitable to attain lift and take off.

I'm sorry Rinky, but you are wrong. You need to mentally disconnect the ground from the plane. Using your cue I will try it this way. If a plane is facing forward into a 200 mph wind, engines off, will it fly? Yes, straight up. The plane will attain lift and take off straight up, untill someone applies enough force to overcome the difference between lift and gravity and bring it back down.

I already tried to make a free-body diagram, but couldn't do it here. If I have to I will draw it in paint and load it into photobucket so I can link it here.