Help in strain energy calculation

  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. Mapes

    Mapes 2,532
    Science Advisor
    Homework Helper
    Gold Member

    Given the conditions you've described, the book answers seems to be incorrect.
     
  4. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    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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