Brainteaser Options

[james]

Here's a question for you:

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

A couple of links discussing it (and some funny rationalizations for peoples incorrect assumptions):
www.kottke.org/06/02/plane-conveyor-belt
www.straightdope.com/columns/060203.html

[james]

I don't understand that post Mike - on a freewheeling system why would increasing the speed of the conveyor increase the friction or drag (apart from so minutely as to make no difference to the model)?

The rope pulling example Em gave above is probably the best analogy I can think of too:
The rope is the motive force (like the engines pushing air out the back of the plane) and as the friction of the wheel bearings is negligible once inertia has been overcome.
The force exerted by the engines (or pulling the rope) will be greater than any friction in the wheels - thats why they have wheels.
The fact that the conveyor speeds up is also irrelevant (so many people fixating on the irrelevant parts of the question) - try this example:

Using the treadmill, say it starts running at 20mph and you pull yourself forward at 2 mph, depending on how often the feedback system updates the speed controller in the conveyor, the treadmill speed will go up, but that makes no difference to you pulling yourself along the rope.
Now try it with the treadmill at 100mph, or 500mph - or whatever. Unless the wheels seize up they will always spin around at whatever the speed of the treadmill is plus your forward velocity caused by pulling on the rope, but none of that matters to what happens on the rope.