Question

A steel rod 2.0m long has a cross sectional area 0.30cm³. The body is now hung by one end from a support structure and 550kg melting machine is hung from the rod lower. If the elongation is 1.8mm, determine the young modulus of the steel (g=9.8m/s²)

Answer 1

length of steel rod , L = 2m

cross sectional area , A = 0.3 cm² = 0.3 × 10^-4 m²

tension acting on steel wire, T = mg = 550 × 9.8 = 5390 N

strain = ∆l/L = 1.8mm/2m = 1.8 × 10^-3/2 = 0.9 × 10^-3 m

now, Young's modulus , Y = T/{A × strain}

= 5390/{0.3 × 10^-4 × 0.9 × 10^-3}

= 5390/(0.27) × 10^7

= 19962.9 × 10^7

= 1.9962 × 10¹¹ N/m²

hence, Young's modulus of the steel is 1.9962 × 10¹¹ N/m²