Describe how to determine Young modulus for a metal wire, including diameter, gauge length, small extensions, loading procedure, graph, control of systematic effects, safety and uncertainty. A graph of F against x has slope 8.0 × 10³ N m⁻¹ for L=1.50 m and d=0.300 mm. Determine E; state how a 2% diameter uncertainty contributes to its percentage uncertainty.

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E=kL/(πd²/4)=1.70 × 10¹¹ Pa. Diameter contributes 4% because E∝d⁻². The procedure needs zero-corrected multi-position micrometer readings, a long wire and extension gauge, incremental elastic loading and a controlled reference/baseline. Specify rigid support, long wire, hanger/known masses, length scale, micrometer and sensitive extension reading. Measure initial gauge length, and mean zero-corrected diameter at several positions/orientations. Preload, record baseline, load incrementally, wait, repeat/unload and remain elastic. Control temperature/support movement/clamp slip; use reference wire or equivalent check. Graph F vs x in SI; k=EA/L, so E=4kL/(πd²). Substitute to obtain 1.70 × 10¹¹ Pa. Double fractional diameter uncertainty: 4%; include gradient and length uncertainties for total. Give relevant snapping-wire/falling-mass precautions.

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