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Energy equations

  1. Jan 22, 2012 #1
    I was just wondering, why do the energy equations look so alike?
    Refering to kinetic energy, the energy stored by capacitors and inductors, etc.
    My teacher in electromagnetism said something about it, that there's a reason for this.
    The energy is proportional to some rate of change squared?
  2. jcsd
  3. Jan 22, 2012 #2

    Philip Wood

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    Gold Member

    In all the cases you've mentioned we have an underlying linear relationship (e.g. between charge and voltage for a capacitor, momentum and velocity for a moving body), and the energy is found as the area of a triangle underneath the linear graph, or, algebraically as the integral of kx wrt x. Hence the 1/2.

    [Where we don't have the linear relationship (e.g. the non-linear momentum-velocity relationship in Special Relativity) we don't get the (1/2) k x^2 form for energy]
    Last edited: Jan 23, 2012
  4. Jan 22, 2012 #3
    Usually you'll find kinetic energy to be quadratic in velocities
    depends where you're coming from really, it could be a 'it just is' matter or it could be because the action in relativity is proportional to the integral of arclength. you could perhaps argue that it must be velocities squared because it shouldn't matter which direction the velocity is in
    there are lots of reasons that it should be in the form that it is but would it be possible to say which is the cause of it's form and which are the cause of it's form? I'd guess not
    the potential energy doesn't have this same standard form however, it can be any function of coordinates you want it to be

    just my two cents
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