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14 April, 22:15

Use Hooke's Law to determine the variable force in the spring problem. A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 40 centimeters to 70 centimeters?

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  1. 15 April, 01:41
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    Work Done = 67.5 J

    Explanation:

    First we find the value of spring constant (k) using Hooke's Law. Hooke's is formulated as:

    F = kx

    where,

    F = Force Applied = 450 N

    k = Spring Constant = ?

    x = Stretched Length = 30 cm = 0.3 m

    Therefore,

    450 N = k (0.3 m)

    k = 450 N/0.3 m

    k = 1500 N/m

    Now, the formula for the work done in stretching the spring is given as:

    W = (1/2) kx²

    Where,

    W = Work done = ?

    k = 1500 N/m

    x = 70 cm - 40 cm = 0.3 m

    Therefore,

    W = (1/2) (1500 N/m) (0.3 m) ²

    W = 67.5 J
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