An object with density ?0 and mass m is floating in a pool of fluid with density

Question

An object with density ?0 and mass m is floating in a pool of fluid with density ?F. Derive an expression for the volume of the object that is above the fluid. Hint: Archimedes' Principle says that the magnitude 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. Notice that the only knowns in this problem are ?0, ?F , and m. As always, simplify your answers as much as possible.

Explanation / Answer

The final equation is v = (p0/pF) V where V is the ball volume and v is the volume of displaced fluid. So the amount above is U = V - v = (1 - p0/pF)V. QED. We find v from B = pF g v = p0 g V = W which is the weight of the ball. B is buoyancy. When B = W, objects float. As you can see, the g's drop out and v = (p0/pF) V follows for things that float.

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