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sy21_nov14_07hc

# sy21_nov14_07hc - Fluids elasticity matter Newtonian...

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Fluids, elasticity, matter Newtonian mechanics of deformable media Fluids: a problem A beaker contains a thick layer of oil (shown in green) of density ρ 2 floating on water (shown in blue), which has density ρ 3 . A cubical block of wood of density ρ 1 with side length L is gently lowered into the beaker, so as not to disturb the layers of liquid, until it floats peacefully between the layers, as shown in the figure. What is the distance d between the top of the wood cube (after it has come to rest) and the interface between oil and water? Hint: After the wood block has come to rest, it is in static equilibrium. Thus, the magnitude of the buoyant force (directed upward) must exactly equal the magnitude of the gravitational force (directed downward). The buoyant force will depend on the quantity d that you are trying to find. The total buoyant force has two contributions, one from each of the two different fluids. To find the total buoyant force, imagine that the wood block is divided into two pieces, one in oil and one in water. Apply Archimedes' principle to each, and add the two buoyant forces to find the total force. F

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sy21_nov14_07hc - Fluids elasticity matter Newtonian...

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