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Step 1 — Identify the type: Is it about elongation (use Y), shape change (use G), or volume change (use B)? Most wire problems use Y.

Step 2 — Write the appropriate formula: Y = FL/(ADelta L) is the workhorse. Remember A = pid^2/4 = pi*r^2.

Step 3 — Series vs parallel: Wires in series (same force, different extensions) — add elongations. Wires in parallel (same extension, different forces) — add spring constants k = YA/L.

Step 4 — Energy problems: Choose the form U = F^2L/(2AY) when force is given, or U = YA(Delta L)^2/(2L) when extension is given.

Step 5 — Unit consistency: Always convert mm to m, cm^2 to m^2 before calculating. Common conversions: 1 mm = 10^{-3} m, 1 cm^2 = 10^{-4} m^2, 1 GPa = 10^9 Pa.

Common traps: (1) Elongation is inversely proportional to Y, not directly. (2) Breaking force depends on area, not length. (3) When a wire is drawn to n times its length (volume constant), new elongation under same force = n^2 times original. (4) Wire under its own weight: use half the weight and full length, giving Delta L = MgL/(2AY). (5) Thermal stress is independent of length. (6) Young's modulus is a material property — changing dimensions doesn't change Y.