Problem 1.52 - Problem 1.52[Difficulty 4 Given American...

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Problem 1.52 [Difficulty: 4] Given: American golf ball, m = 1.62 ± 0.01 oz, D = 1.68 in. Find: Precision to which D must be measured to estimate density within uncertainty of ± 1percent. Solution: Apply uncertainty concepts Definition: Density, 3 3 D m 4 3 6 R π ρ π ∀ = = Computing equation: 1 2 1 2 1 R x 1 R u u R x x = ± + L From the definition, 3/6 3 6 m m D D (m, D) π π ρ ρ = = = Thus m m 1 ρ ρ = and D D 3 ρ ρ = , so 1 2 2 2 m D 2 2 2 m D u [(1u ) (3 u ) ] u u 9 u ρ ρ = ± + = + Solving, 1 2 2 2 1 D m 3 u [u u ] ρ = ± From the data given,
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