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In 2012, film producer James Cameron (Terminator, Titanic, Avatar) rode his submersible Deepsea Challenger to the bottom of the 11-km-deep Marianas Trench, the deepest spot in Earth’s oceans. Cameron could barely fit into Deepsea Challenger’s crew compartment, a steel sphere with inside diameter 109 cm and walls 6.4 cm thick. Find the total pressure force exerted on the sphere at the bottom of the trench. (The total force is the sum of all pressure forces without regard to direction; it’s not the same as the buoyancy force, which is the net pressure force—a vectorial sum.)
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