Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rubber bands and Hooke's Law

  1. Oct 25, 2004 #1
    I have found a website which claims that rubber bands obey a force law
    While this is similar to Hooke's Law in the sense that it *almost* approaches it for large values of x, it is also quite different. Can anyone confirm or deny the formula's reliability? Thanks.
  2. jcsd
  3. Oct 26, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Are you sure [itex]x = L/L_0~~and~not~~\delta L/L_0~[/itex] ?
  4. Oct 26, 2004 #3
    No, I'm not sure.
  5. Oct 26, 2004 #4


    User Avatar
    Homework Helper

    Well if you're familiar with elasticity you can formulate Hooke's Law in its terms,

    Stress = Modulus of Elasticity x Relative Deformation

    For a longitudinal deformation, the modulus is called Young's modulus

    [tex] \sigma = Y \delta L [/tex]

    Since Stress = Force/Area

    [tex] \frac{F}{A} = Y \delta L [/tex]

    [tex] F = YA \delta L [/tex]

    You know

    [tex] \delta L = \frac{\Delta L}{L_{o}} [/tex]

    [tex] F = YA \frac{\Delta L}{L_{o}} [/tex]


    [tex] F = \frac{YA}{L_{o}} \Delta L [/tex]

    we have

    [tex] F = \frac{YA}{L_{o}} \Delta L [/tex]

    Hooke's Law

    [tex] F = k \Delta x [/tex]

    where k in our equation is (x = L)

    [tex] k = \frac{YA}{L_{o}} [/tex]

    The people from that page probably tried something similar, can you give us the website?
    Last edited: Oct 26, 2004
  6. Oct 26, 2004 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    The given formula, in order to be meaningful must have [tex]x=\frac{L}{L_{0}}[/tex]

    Rewritten slightly, it simply says:

    Hence, it predicts a hardening for compression of the rubber.
    I don't know if it actually is good, though..
  7. Oct 26, 2004 #6
  8. Oct 26, 2004 #7


    User Avatar
    Science Advisor
    Gold Member

    Which is what they give under the link. So it looks like a simple uniaxial time-independent hardening mod of sorts ... so is it just a simple made up correction or does it have any theoretical merit ?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook