Six spheres of radius are dropped into a tall jar of oil and each one's terminal…
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory
Computational Physics, Ch Seeing the answer: plots that can be trusted
Problem
Six spheres of radius a are dropped into a tall jar of oil and each one's terminal speed v is measured, repeatable to 0.5 per cent. A power law v=Can is expected. a/mm: 0.50, 1.00, 2.00, 4.00, 8.00, 12.50. v/mms−1: 0.488, 1.905, 7.273, 26.67, 91.43, 192.3. A straight line is fitted to log10v against log10a through all six points, and the residuals of that fit, expressed as percentages of the fitted speed and listed in the same order, are −6.2, +0.8, +5.9, +6.9, +0.9 and −7.5 per cent. The uncertainty of a logarithm is σlog10v=σv/(vln10), and two independent readings combine in quadrature; this chapter does not build either rule.
((a)) Find the exponent the two end readings support, with its uncertainty.
((b)) State how many decades of a the readings span, and say whether this chapter's rule allows the exponent to be claimed from them.
((c)) Say what the residuals add that the slope alone does not, and what they imply about v=Can as a model.