Consider a cylindrical nickel wire 1.6 mm in diameter and 2.5 × 104 mm long. Calculate its elongation when a load of 320 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).

0.192 m

Explanation:

The young's modulus of the Nickel wire is given as,

γ = Stress/Strain

γ = (F/A)/ΔL/L

γ = FL/ΑΔL Equation 1

Where γ = young's modulus of the Nickel wire, F = Load applied, A = cross sectional area of the nickel wire, L = Length of the nickel wire, ΔL = Elongation.

make ΔL the subject of the equation

ΔL = FL/γA Equation 2

Also,

A = πd²/4 Equation 3

d = diameter of the of the wire

Substitute equation 3 into equation 2

ΔL = 4FL/γπd² Equation 4

Given; F = 320 N, L = 2.5×10⁴ mm = 250 m, d = 1.6 mm = 0.0016 m, γ = 207×10⁹ N/m², π = 3.14

Substitute into equation 4

ΔL = (4×320×250)/(207×10⁹×3.14×0.0016²)

ΔL = 320000/1663948.8

ΔL = 0.192 m