A group measured the Young's modulus of a steel wire by the extension method

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Writing the result, and the integrity of the data behind it

Problem

A group measured the Young's modulus of a steel wire by the extension method, obtaining a mean

\bar E = 2.103\times10^{11}\,\mathrm{Pa}

with combined standard uncertainty

u_{\rm c}(E) = 0.058\times10^{11}\,\mathrm{Pa}

(

k=1

). The budget had two components added in quadrature: the travelling-microscope extension reading,

0.054\times10^{11}\,\mathrm{Pa}

, and the wire-diameter measurement,

0.020\times10^{11}\,\mathrm{Pa}

. The accepted value for this grade of steel is

E = 2.00\times10^{11}\,\mathrm{Pa}

, taken as exact for comparison. ((a)) Round the result correctly and state it at

k=2

. ((b)) Compute the consistency ratio

z

between the measured and accepted values. ((c)) Identify the limiting contribution in the budget. ((d)) Write the conclusion sentence: the result with its coverage factor, the comparison, the limiting contribution, and the scope of the result (state that it applies only over the elastic range explored, and should not be extended to strains beyond it).

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