A spring is measured under tension already carrying a preload

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

A spring is measured under tension already carrying a preload, so its restoring force follows

F = F_0 + kx

with

F_0 = 2.5\,\mathrm N

(the preload) and

k = 40\,\mathrm{N\,m^{-1}}

, for extensions

x

from

1\,\mathrm{mm}

500\,\mathrm{mm}

(three decades of

x

). Someone argues: "since

x

spans three decades, log-log axes should be used to fit the whole range onto one page." ((a)) State which of linear, semi-logarithmic or log-log axes actually shows

F

against

x

as a straight line, and justify the choice from the functional form of

F(x)

. ((b)) Explain what is wrong with the argument for log-log axes, given that the data really do span three decades in

x

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