• Tags: Young-modulus, stress, strain
• Difficulty: Moderate

Young's modulus Y = stress/strain = (F/A)/(Delta_L/L) = FL/(ADelta_L). In Searle's apparatus, two identical wires hang side by side: one carries the load (experimental wire), the other serves as a reference (compensates for temperature changes). A spirit level between the wires detects extension. Load the wire in steps, measure extension with the micrometer. Plot load (F) vs extension (Delta_L): slope = YA/L, so Y = slopeL/A. For a wire of diameter d: A = pid^2/4. Measure d using a screw gauge at multiple points. Percentage error: Delta_Y/Y = Delta_F/F + Delta_L_0/L_0 + Delta_(Delta_L)/Delta_L + 2Delta_d/d. The diameter measurement contributes most to error (power of 2 in area). Precautions: remove kinks by loading/unloading before experiment; do not exceed elastic limit; wait for equilibrium after each load increment.