One thing's for sure. After this, we're all going to be a lot thinner!

Classical Mechanics Level 5

A perfectly spherical, but squishable ball of radius \(10~\mbox{cm}\) is blown up to an internal pressure of \(2~\mbox{atm}\). The ball is placed between two perfectly vertical walls and the walls are slowly squeezed together. Initially the ball slips down the walls, but when the walls are \(18~\mbox{cm}\) apart the ball stops slipping down. What is the coefficient of friction between the surface of the ball and the walls?

Details and assumptions

  • The ambient air temperature is \(20^\circ \mbox{C}\).
  • Air has a molar mass of \(29~\mbox{g/mol}\).
  • The mass of the ball (not including any air inside) is \(100~\mbox{g}\).
  • \(1~\mbox{atm}\) is \(101,325~\mbox{Pa}\).
  • The ball squishes as the walls close in, but you may assume the ball does not deform otherwise.
  • The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
  • Hint: the answer is very small.

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