Problem 1.47 - Problem 1.47[Difficulty 3 Given Soda can...

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Problem 1.47 [Difficulty: 3] Given: Soda can with estimated dimensions D = 66.0 ± 0.5 mm, H = 110 ± 0.5 mm. Soda has SG = 1.055 Find: Volume of soda in the can (based on measured mass of full and empty can); Estimate average depth to which the can is filled and the uncertainty in the estimate. Solution: Measurements on a can of coke give m g, m g m m m u g f e f e m = ± = ± = = ± 3865 050 17 5 050 369 . . . . 2 1 2 2 + = e f m e e m f f m u m m m m u m m m m u u 0.5 g 386.5 g u m m f e = ± = ± = ± = 0 00129 050 17 5 0 0286 . , . . . 0019 . 0 0286 . 0 1 369 5 . 17 00129 . 0 1 369 5 . 386 2 1 2 2 ± = × × + × × ± = m u Density is mass per unit volume and SG = ρ / ρΗ 2 Ο so ∀ = = = × × × = × m m H O SG g m kg kg 1000 g m 2 ρ ρ 369 1000 1 1055 350 10 3 6 3 . The reference value ρ H 2 O is assumed to be precise. Since SG is specified to three places beyond the decimal point, assume u SG = ± 0.001. Then ( ) ( ) [ ] mm 102 m mm 10 m 066 . 0 m 10 350 4 4 or 4 % 21 . 0 0021 . 0 001 . 0 1 0019 . 0 1 3 2 2 3 6 2 2 2 1 2 2 2 1 2 2 = × × × = = = ± = ± = × + × ± =
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