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# Elastic Potential Energy

### Elastic Potential Energy

Elastic Potential Energy is the stored energy in an object that is stretched, and can be calculated using an equation.

Can you recall what kind of energy a stretched rubber band or compressed spring has?

Can you guess which of the following is **not** an example of Elastic Potential Energy (**EPE**)?

Only certain materials are 'elastic'. Think about a material being pulled apart or pushed together. Which of the following statements do you think might be true for an elastic material ?

Now we know that an elastic object is restored to its original shape when an external force is removed, can you guess another way in which EPE can be described?

Can you take a guess as to what this "restoring force" most likely depends on?

The restoring force depends on one other thing. Can you guess what this might be?

The restoring force depends on the **stiffness** of the material and **extent** to which it is stretched. The stiffness of an elastic material or spring is called the **spring constant**: $k=\frac{force}{extension}$.

Remember that the spring constant $k$ is defined like this: $k=\frac{force}{extension}$. Can you work out the units of measurement for the spring constant $k$?

The amount of elastic potential energy stored in a coil compressed by $0.2m$ with spring constant $k=2$ is $EPE=\frac{1}{2}\times2 N/m\times(0.2 m)^2=0.04 J$

Can you have a go at working out the EPE of a coil with spring constant $4 N/m$ and compressed by $1m$ ? Look at the hint if you are unsure.

What do you think the equation for the elastic potential energy (EPE) might be? Look at the hint if you are unsure.

$EPE=\frac{1}{2}\times k\times e^2$. Any elastic material can store EPE if it's shape is stretched, compressed or otherwise changed by an external force, **assuming** it has not been stretched beyond its elastic limit, beyond which it won't return to its original shape.