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17 January, 21:28

Use Hooke's Law to determine the work done by the variable force in the spring problem. Nine joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.40 meter.

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  1. 17 January, 21:29
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    29.16 J

    Explanation:

    From Hook's law,

    W = 1/2 (ke²) ... Equation 1

    Where W = work done, k = Spring constant, e = extension.

    Given: W = 9 J, e = 0.5 m.

    Substitute into equation 1

    9 = 1/2 (k*0.5²)

    Solve for k

    k = 18/0.5²

    k = 72 N/m.

    The work done required to stretch the spring by additional 0.4 m is

    W = 1/2 (72) (0.4+0.5) ²

    W = 36 (0.9²)

    W = 29.16 J.
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