1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Work of a Spring Derivation

  1. Jan 29, 2013 #1
    1. The problem statement, all variables and given/known data
    A spring with stiffness k and unstretched length L is stretched so the elongation is d = x2 - L. A force is applied to make the final length of the spring x2. What is the work done by the force in terms of d?

    2. Relevant equations
    W = F * d = F*dx
    d = x2 - L
    F = k*dx

    3. The attempt at a solution
    Assuming W = F*dx and F = k*dx, then I derived F = k(x2 - L) = k*d

    And plugging F back into the work equation, I got W = (kd)*d which is W = kd^2.

    However, isn't the actual equation for work done by a spring W = (kx^2)/2? I can't seem to find where I missed the factor of 1/2. Any help greatly appreciated!
     
  2. jcsd
  3. Jan 29, 2013 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You assumed in your derivation that the force was constant and equal to its maximum value. Not so. As the spring is stretched, the force starts at zero and only reaches k*d at its full extension.
     
  4. Jan 29, 2013 #3
    Thanks Doc. So in this case would I simply integrate to find W? As in W = integral (F*dx)

    and then W = integral(kxdx) = (kd^2)/2 ...?
     
  5. Jan 29, 2013 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Exactly.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Work of a Spring Derivation
  1. Elastic spring (Replies: 11)

Loading...