It takes 130 J of work to compress a certain spring 0.10m. (a) What is the force constant of this spring? (b) To compress the spring an addi

Question

It takes 130 J of work to compress a certain spring 0.10m. (a) What is the force constant of this spring? (b) To compress the spring an additional 0.10 m, does it take 130 J, more than 130 J or less than 130 J? Verify your answer with a calculation.

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Kim Chi 5 years 2021-07-13T09:35:01+00:00 1 Answers 175 views 1

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  1. thuhuong
    0
    2021-07-13T09:36:51+00:00
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    Explanation:

    Given that,

    Work done to stretch the spring, W = 130 J

    Distance, x = 0.1 m

    (a) We know that work done in stretching the spring is as follows :

    W=\dfrac{1}{2}kx^2\\\\k=\dfrac{2W}{x^2}\\\\k=\dfrac{2\times 130}{(0.1)^2}\\\\k=26000\ N/m

    (b) If additional distance is 0.1 m i.e. x = 0.1 + 0.1 = 0.2 m

    So,

    W=\dfrac{1}{2}kx^2\\\\W=\dfrac{1}{2}\times 26000\times 0.2^2\\\\W=520\ J

    So, the new work is more than 130 J.

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