Suppose that 2 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 46 cm. (a) How much work (in J) is ne

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Suppose that 2 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 46 cm. (a) How much work (in J) is needed to stretch the spring from 37 cm to 41 cm

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RI SƠ 4 days 2021-07-18T23:17:55+00:00 1 Answers 2 views 0

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    2021-07-18T23:19:03+00:00

    Answer:

    the work required is 0.163 J

    Explanation:

    Given;

    Energy applied to the spring, E = 2 J

    initial length of the spring, x₀ = 32 cm

    final length of the spring, x₁ = 46 cm

    Extension of the spring, Δx = x₁ – x₀ = 46 cm – 32 cm = 14 cm = 0.14 m

    The spring constant is calculated as follows;

    E = ¹/₂kΔx²

    k = \frac{2E}{(\Delta x)^2} = \frac{2\times 2}{(0.14)^2} = 204.1 \ N/m^2

    The extension of the spring when it is stretched from 37 cm + 41 cm:

    Δx =  41 cm – 37 cm = 4 cm = 0.04 m

    The work required:

    W = ¹/₂kΔx²

    W = ¹/₂ x (204.1) x (0.04)²

    W = 0.163 J

    Therefore, the work required is 0.163 J

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