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

Young's modulus Y = $\frac{stress}{strain}$ = $\frac{F/A}{(Delta_L/L)}$ = $\frac{FL}{A*Delta_L}$. 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 = $\frac{YA}{L}$, so Y = slopeL/A. For a wire of diameter d: A = pi$d^2$/4. Measure d using a screw gauge at multiple points. Percentage error: $Delta_Y$/Y = $\frac{Delta_F}{F}$ + Delta_L_0/$L_0$ + Delta_$\frac{Delta_L}{Delta_L}$ + 2*$Delta_d$/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.