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30 October, 05:47

Problem 1: A 150 kg person stands on a compression spring with spring constant 10,000 N/m and nominal length of 0.50. What is the total length of the loaded spring?

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  1. 30 October, 05:49
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    The total length of the spring is 0.65 m

    Explanation:

    Hooke's Law

    Hooke's law is use to determine the increment of a spring that is acted upon by a force which is either compression or expansion. Hooke's law states that for a spring undergoing deformation, the force applied is directly proportional to the deformation experienced by the spring. Hooke's law is represented thus;

    F = k x ... 1

    where F is the force applied to the spring

    k is the spring constant

    x is the spring stretch or extension

    Calculations

    The extension x can be obtained by making x the subject formula in equation 1;

    x = F/k

    but F = m x g

    so, x = (m x g) / k

    given that, the mass of the person m = 150 kg

    g is the acceleration due to gravity = 9.81 m/

    k is the spring constant = 10000 N/m

    then x = (9.81 m / x 150 kg) / 10000 N/m

    x = 0.14715 m

    the extension experienced by the spring after the compression is

    0.14715 m

    The total length of the spring would be;

    L = extension + nominal length

    L = 0.14715 m + 0.5 m = 0.64715

    L ≈ 0.65 m

    Therefore the total length of the spring would be 0.65 m
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