A wind-tunnel measurement of the drag force on a body is expected to follow for some…

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Data analysis and model fitting in the laboratory

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Problem

A wind-tunnel measurement of the drag force on a body is expected to follow F=cvnF = cv^n for some exponent nn. Two readings, spanning two decades of speed vv, are made: at v1=5.0 m s−1v_1 = 5.0\,\mathrm{m\,s^{-1}}, F1=(2.10±0.05) NF_1 = (2.10\pm0.05)\,\mathrm N; at v2=500 m s−1v_2 = 500\,\mathrm{m\,s^{-1}}, F2=(20500±400) NF_2 = (20500\pm400)\,\mathrm N. Two rules are supplied here, because this chapter does not build the propagation of uncertainties: the uncertainty of a logarithm is σlog⁡10F=σF/(Fln⁡10)\sigma_{\log_{10}F} = \sigma_F/(F\ln10), and the contributions of two independent readings combine in quadrature. Find nn as the slope of log⁡10F\log_{10}F against log⁡10v\log_{10}v, with its uncertainty, and state whether the result is consistent with the quadratic drag law F∝v2F\propto v^2 met for a falling body with air resistance.

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