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20 September, 23:34

A 1100 kgkg safe is 2.4 mm above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 52 cm. What is the spring constant of the spring?

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  1. 20 September, 23:40
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    191.36 N/m

    Explanation:

    From the question,

    The Potential Energy of the safe = Energy of the spring when it was compressed.

    mgh = 1/2ke² ... Equation 1

    Where m = mass of the safe, g = acceleration due to gravity, h = height of the save above the heavy duty spring, k = spring constant, e = compression

    Making k the subject of the equation,

    k = 2mgh/e² ... Equation 2

    Given: m = 1100 kg, h = 2.4 mm = 0.0024 m, e = 0.52 m

    Constant: g = 9.8 m/s²

    Substitute into equation 2

    k = 2 (1100) (9.8) (0.0024) / 0.52²

    k = 51.744/0.2704

    k = 191.36 N/m

    Hence the spring constant of the heavy-duty spring = 191.36 N/m
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