Hooke's Law

Hooke's Law

Forces can cause objects to deform (i.e. change their shape). The way in which an object deforms depends on its dimensions, the material it is made of, the size of the force and direction of the force.

If you measure how a spring stretches (extends its length) as you apply increasing force and plot extension (e) against force (F);

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the graph will be a straight line.

Note: Because the force acting on the spring (or any object), causes stretching; it is sometimes called tension or tensile force.

This shows that Force is proportional to extension. This is Hooke's law. It can be written as:

F = ke


F = tension acting on the spring.

e is extension = (l-lo); l is the stretched length and lo is original length, and.

k is the gradient of the graph above. It is known as the spring constant.

The above equation can be rearranged as

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Spring constant = Applied force/extension

The spring constant k is measured in Nm-1 because it is the force per unit extension.

The value of k does not change unless you change the shape of the spring or the material that the spring is made of.

A stiffer spring has a greater value for the spring constant

We can apply the concept of spring constant to any object obeying Hooke's law. Such an object is called (linearly) elastic.

  1. An elastic object will return to its original form if the force acting on it is removed.
  2. Deformation in an elastic object increases linearly with the force.

In fact, a vast majority of materials obey Hooke's law for at least a part of the range of their deformation behaviour. (e.g. glass rods, metal wires).

Hooke's Law Diagram

In the diagram above, if you extend the spring beyond point P, and then unload it completely; it won't return to its original shape. It has been permanently deformed. We call this point the elastic limit - the limit of elastic behaviour.

If a material returns to its original size and shape when you remove the forces stretching or deforming it (reversible deformation), we say that the material is demonstrating elastic behaviour.

If deformation remains (irreversible deformation) after the forces are removed then it is a sign of plastic behaviour.