A wire of length \(5.00 \mathrm{m}\) with a cross-sectional area of $0.100 \mathrm{cm}^{2}\( stretches by \)6.50 \mathrm{mm}\( when a load of \)1.00 \mathrm{kN}$ is hung from it. What is the Young's modulus for this wire?

Question: Calculate the Young's modulus for a material given the following information: the length of the wire is 4 m, its cross-sectional area is 2 cm², an elongation of 3 mm occurred under a load of 3 kN. Solution: Step 1: Calculate Stress Force (F) = 3 kN * 1000 = 3000 N Area (A) = 2 cm² * (0.01 m/cm)^2 = 0.0002 m² Stress (σ) = F / A = 3000 N / 0.0002 m² = 15,000,000 N/m² or 15,000,000 Pa Step 2: Calculate Strain Elongation (ΔL) = 3 mm * 0.001 m/mm = 0.003 m Original length (L) = 4 m Strain (ε) = ΔL / L = 0.003 m / 4 m = 0.00075 Step 3: Calculate Young's Modulus Young's modulus (Y) = σ / ε = 15,000,000 Pa / 0.00075 = 20,000,000,000 Pa or 20 GPa The Young's modulus for the material is 20 GPa.