# Hooke's law (Physics question)

#### TheAngryMutant

##### Junior Member
My first year physics text says that F= -kx only works for small displacements. And I didn't want to post on sci.physics, which is a real mess. So, does anyone know how exactly to relate force and displacement for springs? I would imagine it involves the stress and strain characteristics of the substance somehow...

It doesn't seem similar to pendulum, where the accepted approximation is torque = -mgL sin (theta) = -mgL (theta) for small theta.

#### highwire

##### Senior member
A spring will have properties that depend basically on just two things: the material's modulus (stiffness) and the geometry of the spring. A coil spring will be rated in, say pounds per inch, a torsion bar maybe foot pounds per degree.

The spring geometry is usually dealt with by using a spring formula. I have them here ( somewhere), if that is your question.

#### highwire

##### Senior member
And, springs are designed so that the spring material remains within its proportional limit ( elastic range). So, one number, stress/strain or modulus of elasticity for a given material is used. For steel, the value is aprox. 29 million.
An ordinary spring is quite linear. I.E a spring based scale can be used to acurately measure force over a considerable range by displaying the spring displacement.

#### VTHodge

##### Golden Member
The equivalent stiffness for a coil spring is

K = (G * D^4) / (8 * N * d^3)

Where N is the number of active coils. In a compression spring, some coils can become inactive. This is one case where the model of F = -Kx would fail.

Overall it is a good model.

#### Shalmanese

##### Platinum Member
Basically, whent he spring reaches a limit, in no longer is elastic. You have permenatly deformed the spring and it will never retract to its original length.

Its to do with you breaking the bonds basically.

#### RSMemphis

##### Golden Member
Basically, any complicated relationship (and the relationship depends on the spring) can be approximated by a Taylor series:

F = a x + b x^2 + c x^3 + d x^4 ...

where a = - k for Hooke's law.

For x very small, you can neglect the higher order terms (linearizing a problem).
As soon as the spring becomes inelastic, higher order terms need to be included.

Hope that helps.

#### Def

##### Senior member
For first year physics, F = -kx will work for all related spring problems. Also remember energy of a spring is U = 1/2*k*x^2.

That's about all you need to know for First year physics.

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