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Propagation of uncertainties Formulas and graphs

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Volume of a cylinder 12 3456 D = (2.9 ± 0.16) cm D = 2.9 cm D = 0.05 cm+ 0.01 cm+ 0.1 cm 12 3456 h = 1.5 cm h = 0.05 cm+ 0.01 cm+ 0.05 cm h = (1.5 ± 0.11) cm

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Volume of a cylinder D = (2.9 ± 0.16) cm h = (1.5 ± 0.11) cm Result will have 2 significant figures V = ¼ D 2 h V = ¼ (2.9 cm) 2 1.5cm V = 9.907789463 cm 3 V = 9.9 cm 3 How sure can we be about the result? Lowest end: D=2.74 cm, h= 1.39cm V = 8.2 cm 3 (-17%) Highest end: D=3.06 cm, h= 1.61cm V = 11.8 cm 3 (+19 %)

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Using physical quantities with uncertainty in a formula leads to calculation results with an uncertainty. How much uncertainty? How does the formula influence this uncertainty? Is there a way to predict this? Volume of a cylinder

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Uncertainties and functions V = ¼ D 2 h d V D V D+ DD- D DD VV Uncertainty in volume arising from uncertainty in diameter:

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Propagation of uncertainty V = ¼ D 2 h Uncertainty in V = contribution from D + contribution from h Every regular equation has an error equation. Every error equation has one term for each measured quantity.

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Volume of a cylinder D = (2.9 ± 0.16) cm h = (1.5 ± 0.11) cm V = 9.9 cm 3 V = (9.9 ± 1.9) cm 3 Relative error: V/V 100% = 1.9/9.9 100% = 19%

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