A cylindrical cork, of length and radius , slowly extracted from the neck of a bottle. If the normal pressure per unit of area between the bottle and the unextracted part of the cork at any instant is constant and is equal to P, show that the work done in extracting it is , where is the coefficient of friction.

June 15th 2009, 04:57 PM

the_doc

A short one for a change!

The solution:

Spoiler:

Let be the amount of the cork that's been extracted so there is of the length of the cork that is not extracted. This part is subject to a constant pressure of and this acts on the curved surface of the cork. This surface has area of so the total force (normally) against the glass of the bottle is