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19 May, 13:55

Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 35 cm to a length of 52 cm. How much work is needed to stretch it from 45 cm to 55 cm? Your answer must include the correct units.

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  1. 19 May, 16:58
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    2.08 J

    Explanation:

    From Hook's law,

    The expression for the work required to stretch a spring is given as,

    W = 1/2ke² ... Equation 1

    Where W = Work require to stretch the spring, k = spring constant of the spring, e = extension.

    make k the subject of the equation

    k = 2W/e² ... Equation 2

    Given: W = 2 Joules, e = 52-35 = 17 cm = 0.17 m

    Substitute into equation 2

    k = 2*2 / (0.17²)

    k = 138.41 N/m

    First the work needed to stretch it to 45 cm

    W = 1/2ke²

    Where k = 138.41 N/m, e = 45-35 = 10 cm = 0.1 m

    Substitute into equation above

    W = 1/2 (138.41) (0.1²)

    W = 0.69205 J.

    Also the work needed to stretch the spring to 55 cm

    Given: e = 55-35 = 20 cm = 0.2 cm

    W' = 1/2 (138.41) (0.2²)

    W' = 2.7682.

    Hence the work needed to stretch the spring from 45 cm to 55 cm = 2.7682-0.69205 = 2.08 J
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