ELASTICITY OF SOLIDS
 

Some solids can be stretched or compressed more easily than others. A piece of copper wire, for example, can be stretched, although a similar length of rubber band can be stretched much more. However, there is a difference in the stretchiness of these two substances that goes beyond mere extent. If you let go of a rubber band after stretching it, it will spring back to its original length, but if you let go of a copper wire, it will stay stretched.

The elasticity of a substance is the extent of its ability to return to its original dimensions after a sample of it has been stretched or compressed. According to this definition, rubber has high elasticity, and copper has low elasticity. Note that elasticity, defined in this way, is qualitative (it says something about how a substance behaves) but is not truly quantitative (we aren’t assigning specific numbers to it). Scientists can and sometimes do define elasticity according to a numerical scheme, but we won’t worry about that here. It is worth mentioning that there is no such thing as a perfectly elastic or perfectly inelastic material in the real world. Both these extremes are theoretical ideals.
This being said, suppose that there does exist a perfectly elastic substance. Such a material will obey a law concerning the extent to which it can be stretched or compressed when an external force is applied. This is called Hooke’s law: The extent of stretching or compression of a sample of any substance is directly proportional to the applied force. Mathematically, if F is the magnitude of the applied force in newtons and s is the amount of stretching or compression in meters, then
s = kF
where k is a constant that depends on the substance. This can be written in vector form as
s = kF
to indicate that the stretching or compression takes place in the same direction as the applied force.
Perfectly elastic stuff can’t be found in the real world, but there are plenty of materials that come close enough so that Hooke’s law can be considered valid in a practical sense, provided that the applied force is not so great that a test sample of the material breaks or is crushed.