Consider a cylindrical nickel wire 2.3 mm in diameter and 2.6 × 104 mm long. Calculate its elongation when a load of 260 N is applied. Assume that the deformation is totally elastic and that the elastic modulus for nickel is 207 GPa (or 207 × 109 N/m2)

7.255 × 10 ⁻³ m

Explanation:

Using the formula

elastic modulus = stress / strain

strain = stress / elastic modulus

stress = F / A

A = πr² = 3.142 × ( 2.3 mm / 2 × ( 1 m / 1000 mm))² = 0.0000041553 m²

Stress = 260 N / 0.0000041553 m² = 62570768.14 N/m²

strain = 62570768.14 N/m²  / 207 × 10 ⁹ N/m² = 3.023 × 10 ⁻⁴

strain = ΔL / L

where L = 2.6 × 10 ⁴ mm = 2.6 × 10 ⁴ mm  × 1 m / 1000 mm = 26 m

3.023 × 10 ⁻⁴  = ΔL / 26 m

ΔL = 3.023 × 10 ⁻⁴ × 26 m = 7.86 × 10 ⁻³ m

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