Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 1 - Introduction, Measurement, Estimating - General Problems - Page 20: 55

Answer

(a) The percent uncertainty in $\theta$ is 3%. The percent uncertainty in $sin(\theta)$ is 3%. (b) The percent uncertainty in $\theta$ is 0.7%. The percent uncertainty in $sin(\theta)$ is 0.2%.

Work Step by Step

(a) $\frac{0.5^{\circ}}{15^{\circ}}\times 100\% = 3\%$ $\frac{sin(15.0^{\circ} - sin(14.5^{\circ}))}{sin(15.0^{\circ})}\times 100\% = 3\%$ The percent uncertainty in $\theta$ is 3%. The percent uncertainty in $sin(\theta)$ is 3%. (b) $\frac{0.5^{\circ}}{75^{\circ}}\times 100\% = 0.7\%$ $\frac{sin(75.0^{\circ} - sin(74.5^{\circ}))}{sin(75.0^{\circ})}\times 100\% = 0.2\%$ The percent uncertainty in $\theta$ is 0.7%. The percent uncertainty in $sin(\theta)$ is 0.2%.
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