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20 October, 11:52

A box of mass m = 1.80 kg is dropped from rest onto a massless, vertical spring with spring constant k = 2.00 ✕ 102 N/m that is initially at its natural length. How far is the spring compressed by the box if the initial height of the box is 2.25 m above the top of the spring?

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  1. 20 October, 12:20
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    spring compressed is 0.724 m

    Explanation:

    given data

    mass = 1.80 kg

    spring constant k = 2 * 10² N/m

    initial height = 2.25 m

    solution

    we know from conservation of energy is

    mg (h+x) = 0.5 * k * x² ... 1

    here x is compression in spring

    so put here value in equation 1 we get

    1.8 * 9.8 * (2.25+x) = 0.5 * 2 * 10² * x²

    solve it we get

    x = 0.724344

    so spring compressed is 0.724 m
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