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.