Snakes on a Plane on a Conveyor Belt: Will it Blend?

This is getting out of hand.  Gruber links to Kottke who has live-blogged a Mythbusters episode about the plane on a conveyor belt riddle.  (Mythbusters must be running out of myths to bust.)  There are nearly 300 raging comments on Kottke’s original post alone, with other forums similarly ablaze.

The thing is, this is SO easy once you recognize that it’s just a trick question; the whole point of this riddle is that it’s a trick question.  The riddle says that there’s a plane on a giant conveyor belt runway, and the conveyor belt has a control system which keeps the belt moving backwards at the same speed that the plane itself is moving forward.  The question is: will the plane take off?

The Simple 4-Sentence Solution:

The bit about the belt moving backwards at the same speed is supposed to make you think that the plane isn’t moving relative to the real ground and the earth.  If that were the case, then of course the plane would not take off.  However, the force generated by the belt does not translate to backwards force on the plane, because a plane’s wheels are free-spinning: as the belt moves, the plane’s wheels spin, rather than remaining stationary so the plane itself can move backwards.

There would be some small amount of backwards force on the plane itself due to friction on the axles of the wheels, but that has virtually no effect on the plane’s forward motion because it’s such a tiny force relative to the forward-thrust of the plane’s engines.

The comments on these other sites are full of debates about airfoils and Bernoulli’s Principle and what really makes a plane fly; all of those people have missed the trick in this riddle (the free-spinning wheels) and so are over-complicating the problem.