Rubber bands and Hooke's Law

  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. Gokul43201

    Gokul43201 11,141
    Staff Emeritus
    Science Advisor
    Gold Member

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

    Pyrrhus 2,276
    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. arildno

    arildno 12,015
    Science Advisor
    Homework Helper
    Gold Member

    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. PerennialII

    PerennialII 1,102
    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 ?
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?
Similar discussions for: Rubber bands and Hooke's Law