Re: Airplane question - cup stays still on table - Saab General Bulletin Board - Saabnet.com
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Re: Airplane question - cup stays still on table
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Posted by jeff in MD (more from jeff in MD) on Fri, 30 Jul 2010 07:28:58 Share Post by Email
In Reply to: Airplane question - cup stays still on table, bender [Profile/Gallery] , Fri, 30 Jul 2010 07:13:45
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When turning, the plane is accelerating towards the center of an imaginary circle. The force pushing the plane in that direction is the centripetal force. This force is applied to the cup (and everything else on the plane) by the surfaces they're in contact with. In the cup's case, there's a normal force pushing up from the tray, and a friction force parallel to the tray. The sum of those two forces and the force of gravity pulling down on the cup equal the centripetal force.

If the plane was level, only the friction forces would contribute to the centripetal force. The friction force is a fraction of the normal force (the fraction defined by the coefficient of friction), so there's a pretty low limit before things start sliding if the plane is level. Leaning the plane over does two things: it increases the normal force, thus increasing the friction, and it causes a contribution to the centripetal force from the normal force, so less friction is required to keep the cup from sliding. So things stay put.

Same things that explain why they bank highway turns, or why you lean over when turning on a motorcycle.

This would all be much easier to explain withs some diagrams! :)

jeff

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