On the deck of a boat a wine flask and parially filled with lead shot (so it will sink) and then corked and thrown overboard. The cork has a radius of 1.59 cm. A force of 553.885 Newtons is required to overcome the friction on the cork.

(a) At what depth would the water pressure push the cork into the bottle? This is sometimes referred to as the "crush depth". (b) Suppose that in addition to the lead shot the flask is partially filled with champagne so that its contents are under a pressure of 112.967 PSI (gauge) from all the 'bubbly'. At what depth during its descent into the ocean would it succumb?