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Where does spring (Hooke's law) energy come from?

  1. Jan 23, 2009 #1
    I'm talking about just any kind of F = k.x spring, with E = 1/2 k x ^2. Why can doors be closed by something that appears to have no energy source? Why can automatic guns reload requiring a battery source? (okay, maybe a bad example because they use the gas produced).
  2. jcsd
  3. Jan 23, 2009 #2

    Andy Resnick

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    Energy is stored as compressive (or tensile) stress due to elastic deformation. Elastic deformation is often represented at the molecular level by springs, but at the atomic level, tensile and compressive stress are stored in terms of molecular rearragement. Going from that detailed level to a macroscopic/thermodynamic description is not simple.
  4. Jan 23, 2009 #3


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    The energy comes from whatever source compresses the spring.

  5. Jan 23, 2009 #4


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    Ie, your arm in the case of the door. That example is simply a manifestation of conservation of energy.
  6. Jan 23, 2009 #5
    Here is how my textbook puts it:

    We can expand the U(x) function, whatever it is, to a Taylor expansion. So,

    U(x) = U(0) + U'(0)x + .5U''(0)x^2 + ...

    As long as x remains small (which is what Hooke's law is accurate for), the first three terms in this series should be a good approximation. The first term is a constant, and, since we can always subtract a constant from U(x) without affecting any physics, we may redefine U(0) to be zero. Because x = 0 is an equilibrium points, U'(0) = 0 and the second term in the series is automatically zero. Because the equilibrium is stable, U''(0) is positive. Renaming U''(0) as k, we conclude that for small displacements it is always a good approximation to take U(x) = .5kx^2.
  7. Jan 23, 2009 #6

    That is true, but i'm more interested in how you get the energy back. For example, you could say for a can falling down on earth, "the person who threw that can in the air gave it the gravitational potential", and that's true, but it doesn't give any insight on how that energy is released if you don't know about gravity.

    Same thing but now about springs.
  8. Jan 23, 2009 #7


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    Refer to post #2 by Andy. He has explained where the energy is stored. It is returned once the force applied to compress it is released. Essentially the deformation it experienced is reversed back to an equilibrium state. The elastic potential energy of the spring moves from a higher ordered state to a lower ordered state (i.e. a higher potential to a lower potential). The spring's natural state is its equilibrium position or zero-potential energy state. The spring "desires" to be there naturally.

    Take a look here for some info on potential energy:


  9. Jan 25, 2009 #8
    Okay, thanks.
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