Remember all those times when you pull back an elastic band, aim it at your sister or brother, and then just let go? Obviously, we would never tell you to do something like this – it would be dangerous, but if you do get a chance then stop to think about the physics that are happening here, there is so much physics happening for you to be able to hear the satisfying yelp of your brother or sister. This is what we are going to look at in this activity. You will learn about the equation for elastic energy and what happens when you pull an elastic band too much (this is called the elastic limit).

So, to start off with, let’s look at the energy transfers that are going into stretching the elastic band. What energy do you need to put into stretching the elastic band and what energy is transferred to when you let go of the elastic band?

INSERT IMAGE

If you thought about kinetic energy for both, then you would have been correct. You need to kinetic energy into the band to store that energy as elastic energy. When you let the band go, the stored elastic energy will go back to being kinetic energy as the band contracts back to its original size.

Okay, so have you ever pulled a spring? Have you ever just kept on pulling the spring? Have you ever pulled a spring so much that it didn’t spring back to its original shape? What happened to the energy then?

You reached the elastic limit of the spring at this point. There was so much energy put into the object that it couldn’t cope, and the particles became deformed within the object. The energy was transferred into the particles in order the rearrange them – it’s not gone, but it is really difficult to get back, the spring is essentially broken.

BROKEN SPRING AND NOT BROKEN SPRING IMAGE.

Now it’s time for the part that you have all been waiting for – the maths!

Our equation this time looks just like some other equations we have looked at:

INSERT EQUATION HERE

E = energy (Joules (J))

k = the spring constant. Each spring will have its own spring constant, and it tells us how much energy a spring can store. A higher spring constant means a spring can store more energy (Newtons per meter (N/m))

x = extension. How far the spring has moved from its original size (meters (m)).

Let’s have a go at a question now:

Jean is doing an experiment with springs. He starts with a spring of length 0.010 m and places masses on it until it reaches a length of 0.015 m. The box of springs says that the spring constant is 200 N/m. Calculate the energy put into the spring from this extension.

**Step 1 – Find all the numbers and highlight them. **

Jean is doing an experiment with springs. He starts with a spring of length 0.010 m and places masses on it until it reaches a length of 0.015 m. The box of springs says that the spring constant is 200 N/m. Calculate the energy put into the spring from this extension.

**Step 2 – Write out the numbers next to their symbols.**

E = ?

k = 200 N/m

x = 0.015 – 0.010 = 0.005 m

We needed to work out the change in x, because x is the change in length (extension) of the spring. So, all you do is take the longest value from the smallest value.

**Step 3 - Put these numbers into the equation:**

E = (0.5 x 200) x (0.005^{2})

**Step 4 – Do the parts in the brackets first. **

E = 100 x 0.000025

**Step 5 – Put do the rest of the equation! **

E = 0.0025 J

**DO NOT** forget the units!