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# Hooke's Law

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## 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);**

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*

* Where:*.

** F** = tension acting on the spring.

** e** is extension = (l-l

_{o}); l is the stretched length and l

_{o}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

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.**

- An elastic object will return to its original form if the force acting on it is removed.
- 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).

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.**