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.