3.48 if we measurethree independent quantities x,y,z and then calculate a function such as q=(x+y)(x+z) then as discussed at the beginning of the section, a stepwise calculation of the uncertainty in q may overestimate the uncertainty delta q
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3.48. *** If we measure three independent quantities x, y, and z and then calculate a function such as q = (x + y)/(x + z), then, as discussed at the beginning of Section 3.11, a stepwise calculation of the uncertainty in q may overestimate the uncertainty ͉q. (a) Consider the measured values x = 20 ± 1, y = 2, and z = 0, and for simplicity, suppose that ͉y and ͉z are negligible. Calculate the uncertainty ͉q correctly using the general rule (3.47) and compare your result with what you would get if you were to calculate ͉q in steps. (b) Do the same for the values x = 20 ± 1, y = -40, and z = 0. Explain any differences between parts (a) and (b).
Sri K.
The quantity $Q$ depends on the measured values a and $b$ in the following ways: (a) $Q=a / b, a=20 \pm 1, b=10 \pm 1$ (b) $Q=2 a+3 b, a=20 \pm 2, b=15 \pm 3$ (c) $Q=a-2 b, a=50 \pm 1, b=24 \pm 0.5$ (d) $Q=a^{2}, a=10.0 \pm 0.3$ (e) $Q=a^{2} / b^{2}, a=100 \pm 5, b=20 \pm 2$ In each case find the value of $Q$ and its uncertainty.
Physics and physical measurement
Graphical analysis and uncertainties
A quantity of interest Q is given by Q= 4*x + y where x and y are measured experimentally. Calculate the uncertainty in Q if x=17.8+_ 1.5 and y= 35.1 +_ 4.5 assume that the errors are uncorrelated and random. Round your answer to 2 decimal places.
Adi S.
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