1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Question on forces and energy

  1. Dec 9, 2009 #1
    I just watched this http://www.youtube.com/watch?v=eVl5zs6Lqy0" video...

    If W = KE ---> Fd = [mv^2] / 2

    If in a spring, force is equal to a constant (k) times how far its been stretched (d), then subbing kd for F in the first equation...

    Kd^2 = [mv^2]/2
    Rearranging, E = kd^2

    But in my textbook, it says that E = 1/2 [kd^2]
    Where did the 1/2 come from? Even in the video, W = Fd, so from the graph, you times F by d, getting a SQUARE, not a triangle, but he says you times F by d, and divide by 2 since your looking at the area (triangle) underneath...

    Any help?
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Dec 9, 2009 #2
    [tex] U = \frac{1}2kx^2[/tex]

    is the potential energy of the spring. You're talking about the kinetic energy.
    Last edited by a moderator: Apr 24, 2017
  4. Dec 9, 2009 #3

    If on a F vs x graph, you want to find work...

    F = k x
    W = F d

    Then shouldn't work = k xd = kx^2?
  5. Dec 9, 2009 #4
    Yes....but the net work is only equal to the change in kinetic energy. What your book is saying (spring's potential energy) has nothing to do with what you're saying. For a conservative force (ie. only a position-dependent force) like Hooke's law, the force will equal the negative gradient of the potential. So now we have:

    [tex] F = -kx[/tex]

    Take integral and get:

    [tex]U = \frac{1}2kx^2[/tex]
    Last edited: Dec 9, 2009
  6. Dec 9, 2009 #5
    https://www.physicsforums.com/latex_images/24/2483850-2.png [Broken]
    whats that big s line thing for lol
    Last edited by a moderator: May 4, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook