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Originally Posted by Elgin Clock
Fn - Force of Conveyer pushing up at the plane (+Y) ...known as Normal Force.
Fg - Force by gravity...
Ft - For this case, thrust of airplanes jets...
Fcb - Force being countered by the conveyer belt...
So.. in this equation.. and using Newton's third law, which states "For every action, there is an equal and opposite reaction."
Fn + -Fg = 0 = no movement in Y direction
Ft + -Fcb = 0 = no movement in X direction
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You're forgetting the coefficient of friction (mu, but I'm going to use u because I don't want to spend the time to figure out how to type mu) in there. The force exerted on the plane by the tredmill will be at the bearings between the wheels and the axles. (We're assuming that the wheels have infinite traction on the ground) So, your Fcb term has to have u.
Fcb = umg or uFg
Where m is the mass of the plane and g is the acceleration due to gravity. If we take the extreme case and say that we have ideal bearings, u will be 0. That would cancel out the Fcb term. Even if we go to the other extreme and say that u is some thing absurdly high, like 1, we still get that Fcb = Fg. I'm not really sure what a plane weighs, but there's a plane that produces more thurst than it weighs (I think the F16).