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Best solution? for work done on a spring.

  1. Jun 11, 2013 #1
    1. The problem statement, all variables and given/known data
    GIVEN: Force constant (k) = 170N/m. Displaced 10cm (0.1m) from equilibrium position.
    REQUIRED: Find the work done on the spring.

    2. Relevant equations
    Solution 1 uses: W = ΔE, & (elastic energy} Ee = 0.5(k)x2, where k is the constant, and x is displacement from equilibrium position.

    Solution 2 uses: W = F(Δd), & (elastic/spring force} Fe = kx, where k is the constant, and x is the displacement from the equilibrium position.

    3. The attempt at a solution
    Please evaluate these solutions & choose the best. Please tell me why. Please correct my misunderstandings. Thanks!

    w = ΔE
    w = Eefinal - Eeinitial
    w = 0.5(k)xfinal2 - 0 {because initial the spring is at the eq. position.)
    w = 0.5(170N/m)(0.1m)2
    w = 0.85J

    w = F(Δd)
    w = Fe(Δd)
    w = kx(Δd)
    w = (170N/m)(0.1m)(0.1m)
    w = 1.7J

    Which solution is better, and why? (It's obvious why the values are different.)
    Please help me understand why/where these approaches are best. (I understand calculus, but I need to understand these concepts, before I use calculus to evaluate.)
  2. jcsd
  3. Jun 11, 2013 #2


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    The second method is wrong, F is not constant during the displacement.
  4. Jun 11, 2013 #3
    Thanks very much! ! !

    Is there a resource you can point me to that explains why the force is not constant? Or, can you tell me why?

    I'm not trying to be difficult, I just want to understand. I really want to be an engineer.
  5. Jun 11, 2013 #4


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    Staff: Mentor

    Just check how you calculated the force at 10cm excitation. What is the force at an excitation of 5cm?
  6. Jun 11, 2013 #5
    (elastic/spring force} Fe = kx, displacement x varies.Hence force is not constant
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