P15_061

# P15_061 - (b) We replace w with 1 . 6 w in the above...

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61. To be as general as possible, we denote the ratio of body density to water density as f (so that f = ρ/ρ w =0 . 95 in this problem). Floating involves an equilibrium of vertical forces acting on the body (Earth’s gravity pulls down and the buoyant force pushes up). Thus, F b = F g = ρ w gV w = ρgV where V is the total volume of the body and V w is the portion of it which is submerged. (a) We rearrange the above equation to yield V w V = ρ ρ w = f which means that 95% of the body is submerged and therefore 5% is above the water surface.
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Unformatted text preview: (b) We replace w with 1 . 6 w in the above equilibrium of forces relationship, and nd V w V = 1 . 6 w = f 1 . 6 which means that 59% of the body is submerged and thus 41% is above the quicksand surface. (c) The answer to part (b) suggests that a person in that situation is able to breathe. (d) The thixotropic property is warning that slow motions are best. Reasonable steps are: lay back on the surface, slowly pull your legs free, and then roll to the shore....
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