Help in strain energy calculation

  1. May 13, 2009 #1
    1. The problem statement, all variables and given/known data
    When a spring fixed at one end is pulled by a force of 8N, the extension is 40mm. Two such springs are joined in series and is pulled to produce a total extension of 40mm. What is the strain energy in the springs.


    2. Relevant equations
    strain energy, U = Fe / 2 or
    U = F2/2k

    *e is the extension while k is the spring constant.

    ( I found this equation online, correct me if this is wrong. )

    3. The attempt at a solution
    I calculate the strain energy of 1 spring first, which is
    8 x 0.04m / 2 = 0.16J

    ------------------------------------------------------
    for one spring, the spring constant should be
    F = ke
    8 = 0.04k
    k = 200

    For two spring, the spring constant is
    1/k = 1/k1 + 1/k2
    1/k = 1/100
    k = 100

    hence, the force used to made an extension of 0.04m is
    F = 100 x 0.04
    = 4N

    Thus, the strain energy is
    U = F2 / 2k
    = 16 / 200
    = 0.08J

    or

    U = Fe /2
    = 4 x 0.04 / 2
    = 0.08J

    The answer provided by the book is 0.32J, which is differ with the answer I calculated, either one string or two strings. Can anyone correct the mistakes I made while doing calculation? Or the answer given is incorrect?
     
  2. jcsd
  3. May 14, 2009 #2

    Mapes

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    Given the conditions you've described, the book answers seems to be incorrect.
     
  4. May 14, 2009 #3

    tiny-tim

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    Welcome to PF!

    Hi Stefenng! Welcome to PF! :smile:

    Yes, your answer looks right

    (though it would have been easier if you'd also used the equation U = ke2/2, and just added the energies in the two halves :wink:)
     
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