13_Physics ProblemsTechnical Physics

13_Physics ProblemsTechnical Physics - Chapter 1 Section...

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Unformatted text preview: Chapter 1 Section 1.7 *P1.48 13 Significant Figures METHOD ONE We treat the best value with its uncertainty as a binomial 21.3 ± 0.2 cm 9.8 ± 0.1 cm , a fa A = 21.3a9.8f ± 21.3a0.1f ± 0.2a9.8 f ± a0.2 fa0.1f cm f 2 . The first term gives the best value of the area. The cross terms add together to give the uncertainty and the fourth term is negligible. A = 209 cm 2 ± 4 cm 2 . METHOD TWO We add the fractional uncertainties in the data. a 0 0 f FGH 21..23 + 9..1 IJK = 209 cm 8 fa A = 21.3 cm 9.8 cm ± P1.49 a f π r 2 = π 10.5 m ± 0.2 m (a) 2 ± 2% = 209 cm 2 ± 4 cm 2 2 = π (10.5 m) 2 ± 2(10.5 m)(0.2 m) + ( 0.2 m) 2 = 346 m 2 ± 13 m 2 a f 2π r = 2π 10.5 m ± 0.2 m = 66.0 m ± 1.3 m (b) 3 P1.50 (a) P1.51 4 a fa m = a1.85 ± 0.02f kg (b) 3 (c) (d) f r = 6.50 ± 0. 20 cm = 6.50 ± 0.20 × 10 −2 m ρ= m c hπ r 4 3 3 also, δ ρ δ m 3δ r = + . ρ m r In other words, the percentages of uncertainty are cumulative. Therefore, af δ ρ 0.02 3 0.20 = + = 0.103 , 6.50 ρ 1.85 ρ= and a 1.85 c hπ e6.5 × 10 4 3 f −2 j m 3 = 1.61 × 10 3 kg m 3 a f ρ ± δ ρ = 1.61 ± 0.17 × 10 3 kg m3 = 1.6 ± 0.2 × 10 3 kg m3 . 2 ...
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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