A solid metal sphere with density ?metal is placed under a fluid and released fr

Question

A solid metal sphere with density ?metal is placed under a fluid and released from rest. The sphere sinks because ?metal >?water. Derive an expression for the magnitude of the initial downward acceleration of the sphere immediately after it is released. Notice that the volume of the sphere is not given, so your answer should not depend on the volume V. Hint: Archimedes's Principle says that the size of the buoyant force on the sphere is equal to the weight of the displaced fluid. Be sure that your derivation includes a free-body diagram showing the forces on the sphere. As always, simplify your answers as much as possible

Explanation / Answer

F_net = ma = (buoyant force) - mg (buoyant force) = V ?water g ?metal = m/V Use the third equation to eliminate V from the second equation, and then substitute the second equation into the first. Finally, solve for a. ma = m (?water/?metal) g - mg a = g (?water/?metal - 1)

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