Why does a spring exert a force -kx on a block?

[quasar987]

Why is it that a spring exerts a force -kx on a block?

Is it because the atoms making the spring themselves are in a stable equilibrium when the spring is at its relaxed lenght, but as soon as it is stretched, for small displacement around the equilibrium position, a "locally hookian" interatomic force appears?

Also, how far from the thruth is it to say that when I stretch my spring a distance 'd', every atom composing the spring gets distanced from its (left) neighbor by a distance d/N, where N is the number of atoms in a row in the direction parallel to the streching.

This would explain why when we strech the spring too much, the force is no longer hookian. It would also explain why cutting a spring in m parts multiplies it's k constant my m and making it m times longer divides it k constant by m.

 

[PBRMEASAP]

What you've described sounds like a very good description of the origin of Young's modulus, which is like the spring constant of a material. I think for an actual spring, the large scale shape of it (helix) plays a critical role in the restoring force. It may not be necessary to go all the way down to the level of atoms to understand where k comes in. But small displacements around configurations of minimum energy is certainly the right idea.

 

[vector3]

I'll add that certain springs are made from a specific steel as well. Not representing myself as metallurgist I have had a number of occasions to actually specify the use of "spring steel"

General info here:

http://en.wikipedia.org/wiki/Spring_steel