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432_Physics ProblemsTechnical Physics

432_Physics ProblemsTechnical Physics - 434 P14.70 Fluid...

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434 Fluid Mechanics P14.70 Let s stand for the edge of the cube, h for the depth of immersion, ρ ice stand for the density of the ice, ρ w stand for density of water, and ρ a stand for density of the alcohol. (a) According to Archimedes’s principle, at equilibrium we have ρ ρ ρ ρ ice ice gs ghs h s w w 3 2 = = With ρ ice 3 kg m = × 0 917 10 3 . ρ w = × 1 00 10 3 . kg m 3 and s = 20 0 . mm we get h = = 20 0 0 917 18 34 18 3 . . . . a f mm mm (b) We assume that the top of the cube is still above the alcohol surface. Letting h a stand for the thickness of the alcohol layer, we have ρ ρ ρ a a w w gs h gs h gs 2 2 3 + = ice so h s h w w a w a = F H G I K J F H G I
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