Anonymous
Anonymous asked in Science & MathematicsPhysics · 9 years ago

# how to derive hookes law formula to solve for k?

Ee=1/2kx^2

K=

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• ?
Lv 4
9 years ago

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

• 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