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19 January, 17:48

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).

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  1. 19 January, 18:02
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    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
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