Homework 11 Solution

The weight of a sphere of radius r and density s is 4

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Unformatted text preview: o great that it manages to balance the object’s weight and any other forces. The weight of a sphere of radius R and density ρs is 4 Fw = πR3 ρs g 3 i (2) If you came up with a slightly different area, that is not a problem - the geometry is not strictly defined in the problem, so you had a choice to either add or subtract 5 cm from the given dimensions. Either way is fine, it does not change the conclusion. If we are in a surrounding fluid of density ρ, we must also account for the buoyant force, equal to the weight of the displaced fluid. This is the same as the expression above if we substitute ρs → ρ 4 B = πR3 ρg 3 (3) The drag and buoyant forces will act in one direction, the weight of the object opposing them. A force balance yields, at terminal velocity, 0 = Fd + B − Fw 4 4 0 = 6πηRv + πR3 ρg − πR3 ρs g 3 3 43 6πηRv = πR (ρs − ρ) g 3 2g 2 v= R (ρs − ρ) 9η (4) (5) (6) (7) The fact that terminal velocity depends on particle size has many interesting technological applications. (As a quick for-instance: http://en...
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