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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


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    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


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    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


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    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


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    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 ?
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