Just a little picture

December 13, 2006

Yes, the plane does take off

I thought we were finished with this thought experiment about a plane on a treadmill, but it has raised its head again recently. Fortunately, Dr. Paul J. Camp of the Spelman College Department of Physics presents the most concise explanation I have read thus far:

I solved this problem in literally less than five seconds by drawing a free body diagram. Anybody who didn't do that as a first step shouldn't be playing the physics game. There is an upward normal force from the road, a downward gravitational force and (eventually) an upward lift force. As long as the plane remains on the ground, these balance because the vertical component of acceleration is zero so the vertical component of the net force is zero. There is a thrust force from the exhaust pushing the engines (yes, I said that right -- Newton's third law) that points horizontally forward, and there is friction backward. What form of friction? The wheel is not sliding or tending to slide on the conveyor belt because the belt moves along with it so there is only rolling friction and it is quite small, certainly smaller than the thrust or the plane wouldn't get off the ground even without a conveyor belt. Add the vectors. The net force is forward, so the acceleration is forward (Newton's second law). All else is math.

Posted by Charles on December 13, 2006 03:23 PM






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