In 1690, Sir Edmund Halley (of comet fame) invented
the diving bell. A drawing is shown at the right. Halley’s bell was
approximately a wooden cylinder about 3 m high and 1 m in diameter.
(For this problem, treat the bell as if it were a cylinder of the indicated
dimensions.)

(a) If the bottom of the bell is held by a rope so that it is completely submerged,
hovering just above the mud at the bottom of a lake 20 m below the surface,
what is the force the water is exerting on the top of the bell?

(b) What is the force the water is exerting on the bottom of the bell?

(c) If the bell and its contents have a mass of 800 kg, how big a weight has to
be added to the bell as ballast in order to keep it from floating up to the
surface?