The pressure inside a bottle of champagne is 4.5 atm higher than the air pressure outside. The neck of the bottle has an inner radius of 1.0 cm. 

(a) What is the frictional force on the cork due to the neck of the bottle? 

(b) The cork (mass 7.5 g) is loosened until the friction force is zero and then released, allowing the cork to shoot out of the bottle. If the cork moves 1.0 cm along the neck of the bottle as the gauge pressure in the bottle decreases from 4.5 atm to zero, estimate the speed at which the cork shoots out of the bottle.