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Anonymous asked in Science & MathematicsPhysics · 9 years ago

how to derive hookes law formula to solve for k?



4 Answers

  • ?
    Lv 4
    9 years ago
    Favorite Answer

    F = - dE/dx = - kx

    So, yes k = ( 1/x) dE/dx

    You could also write the total mechanical energy of a mass attached to this spring as

    E_total = (1/2) k x^2 + (1/2) m v^2

    Since this is a conservative system ( energy is conserved), dE_total / dt = 0

    0 = kx dx/dt + mv dv/dt

    but v = dx/dt , so this cancels out leaving

    0 = kx + m dv/dt

    but dv/dt = a , the acceleration

    Thus F = ma = - kx which is Hooke's Law

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  • rager
    Lv 4
    3 years ago

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  • Anonymous
    9 years ago

    K = force divided by the amount it stretches.

    Source(s): wikipedia for hooks law
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  • 9 years ago

    F = Kx = dE/dx

    K = dE/dx / x

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