# Understanding Elastic Energy

In this worksheet, students will look at how energy can be stored elastically and how to calculate such energy. They will not cover Hookes law or springs in this activity, for this please refer to our worksheet titled 'Understanding forces and elasticity'. Key stage:  KS 4

GCSE Boards:   AQA, AQA Trilogy, AQA Synergy, OCR 21st Century, OCR Gateway, Eduqas

Difficulty level:   ### QUESTION 1 of 10

Remember all those times when you pulled back an elastic band, aimed 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 is happening here. 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 stretch an elastic band too much (this is called the elastic limit).

So to start 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 when you let go of it? If you thought kinetic energy for both, then you would have been correct. You need to put kinetic energy into the band in order 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 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 spring that it couldn’t cope and the particles became deformed within it. The energy was transferred into the particles in order to rearrange them – it’s not gone, but it is really difficult to get back - the spring is essentially broken. Now it’s time for the part that you have all been waiting for – the maths!

Here is the equation for elastic energy:

E = ½kx²

E =  elastic energy in joules (J)
k = the spring constant in newtons per metre (N/m)  Each spring will have its own spring constant which tells us how much energy a spring can store. A higher spring constant means a spring can store more energy.
x = extension in metres (m). How far the spring has moved from its original size.

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 smallest value from the largest value.

Step 3   Put these numbers into the equation:

E = (0.5 x 200) x (0.0052)

Step 4   Do the parts in the brackets first:

E = 100 x 0.000025

Step 5   Do the rest of the equation!

E = 0.0025 J

DO NOT forget the units!

Are you ready for some questions now?

A person is stretching an elastic band.

Name the input energy.

Kinetic

Elastic

Gravitational

Light

Heat

Match the units to the measurements below.

## Column B

Energy (E)
Metres (m)
Spring constant (k)
Newtons per metre (N/m)
Extension (x)
Joules (J)

Peter pulls on a spring in the lab. He finds that when he pulls it to a specific length, it no longer returns to its original shape when he lets go.

Name the process that Peter has caused to happen.

Plastic limit

Elastic limit

Spring limit

Limit of tension

Sian pulls an elastic band 0.5 m. The elastic band has a spring constant of 30 N/m.

Calculate the energy that Sian puts into the stretching of the elastic band.

Plastic limit

Elastic limit

Spring limit

Limit of tension

A car sits on springs that are used for suspension. When the car runs over a bump in the road, the springs compress by 0.05 m.

Calculate the energy that goes into an individual spring in the car wheels.

Mass of car = 1500 kg

Spring constant  = 3000 N/m

Plastic limit

Elastic limit

Spring limit

Limit of tension

A weighbridge is a device that is used to find out the mass of a large vehicle such as a lorry. It works by having a large metal plate which is set on 4 springs. Based on how much the springs compress, you will be able to find out the mass of the lorry. When a lorry pulls onto the weighbridge, it causes a compression of 0.20 m. The springs have a spring constant of 55,000 N/m.

Calculate the energy the lorry has put onto the whole bridge.

Plastic limit

Elastic limit

Spring limit

Limit of tension

What type of energy is being stored by a spring?

An elastic band with a spring constant of 10 N/m is stretched by  0.09 m.

Calculate the energy stored by the band.

A spring has an original length of 0.02 m and is stretched to a new length of 1.04 m. The spring has a spring constant of 30 N/m.

Calculate the energy stored by the spring.

Give you answer to 1 decimal place.

A man falls 15 m in a bungee jump before the bungee becomes tight. He then moves a further 8 m, stretching the band. The bungee is quoted as having a spring constant of 60 N/m

Calculate the energy stored by the bungee.

• Question 1

A person is stretching an elastic band.

Name the input energy.

Kinetic
EDDIE SAYS
Did you get this one correct? You need to move the elastic band to be able to stretch it - when we talk about moving stuff we should be instantly reminded of kinetic energy. It's the big daddy of moving stuff and you need to be able to remember that word. Kinetic is movement and movement is kinetic!
• Question 2

Match the units to the measurements below.

## Column B

Energy (E)
Joules (J)
Spring constant (k)
Newtons per metre (N/m)
Extension (x)
Metres (m)
EDDIE SAYS
If you ever get stuck with these, think about what would make sense and work your way backwards. Extension is a measurement of distance - we also measure distance in metres, so extension must be in metres, right? Good! Next, energy can be measured with a joulemeter, so it must have something to do with a joule? Yes! Finally, the one that is left must be the spring constant. And you've got them all - brilliant!
• Question 3

Peter pulls on a spring in the lab. He finds that when he pulls it to a specific length, it no longer returns to its original shape when he lets go.

Name the process that Peter has caused to happen.

Elastic limit
EDDIE SAYS
You are dealing with elastic stuff in this set of questions, so the answer must have something to do with that right? Okay, but there are a lot of words in there that might confuse you. Let's remove the ones that don't make sense. Three of them follow a pattern and the last result looks a bit odd. Let's ignore that last one - it doesn't fit in with anything else! Now only the first three remain! How are we going to narrow them down? Plastic isn't elastic (it technically means the opposite), so we are left with two. So now it's a 50/50 guess, or you could look back at the Introduction and remember the term elastic limit. Elastic limit is the answer!
• Question 4

Sian pulls an elastic band 0.5 m. The elastic band has a spring constant of 30 N/m.

Calculate the energy that Sian puts into the stretching of the elastic band.

EDDIE SAYS
So, just like with most of our calculation-based questions, this one is about finding the numbers and then trying to put them into the equation. Then doing it all a thousand times until how to answer the question becomes firmly fixed in your head. Find the numbers and write them down: E = ? k = 30 N/m x = 0.5 m Put them into the equation: E = ½kx² E = (0.5 x 30) x (0.5 x 0.5) Do the stuff in the brackets: E = 15 x 0.25 Do the calculation: E = 3.75 J And you're there!
• Question 5

A car sits on springs that are used for suspension. When the car runs over a bump in the road, the springs compress by 0.05 m.

Calculate the energy that goes into an individual spring in the car wheels.

Mass of car = 1500 kg

Spring constant  = 3000 N/m

EDDIE SAYS
So, how do we answer this question? It's simple if you follow the steps! It's almost like we've given you a set of tools to help you to be successful in exams or something... Step 1 Find the numbers: E = ? k = 3000 N/m x = 0.05 m Did you notice that we don't need the mass? It was a red herring to try and put you off! Step 2 Put the numbers into the equation: E = ½kx² E = (0.5 x 3000) x (0.05 x 0.05) Step 3 Do the stuff in the brackets: E = 1500 x 0.0025 Step 4 Finish off with the maths! E = 3.75 J
• Question 6

A weighbridge is a device that is used to find out the mass of a large vehicle such as a lorry. It works by having a large metal plate which is set on 4 springs. Based on how much the springs compress, you will be able to find out the mass of the lorry. When a lorry pulls onto the weighbridge, it causes a compression of 0.20 m. The springs have a spring constant of 55,000 N/m.

Calculate the energy the lorry has put onto the whole bridge.

EDDIE SAYS
This one is a little more complex. There are four springs, so we need to multiply whatever answer we get by four to get the total energy put into the system. Remember - words in bold will get you marks, so keep an eye out for them in the question! Let's have a look at how we could approach this problem. Step 1: E = ? k = 55,000 N/m x = 0.20 m Step 2: E = (0.5 x 55,000) x (0.20 x 0.20) Step 3: E = 27,500 x 0.04 Step 4: E = 1,100 J Then we need to multiply the answer by four to get the total for all of the springs. 1,100 x 4 = 4,400 J
• Question 7

What type of energy is being stored by a spring?

Elastic
EDDIE SAYS
A spring will always store its energy as elastic energy. In fact, any time you have anything being compressed (so long as it is able to spring back to its original shape again), it will be storing its energy as elastic. It's almost like elastic means something, right?
• Question 8

An elastic band with a spring constant of 10 N/m is stretched by  0.09 m.

Calculate the energy stored by the band.

EDDIE SAYS
Did you remember to put your answer to 2 decimal places? Well done if you did! We put it in there to trip you up, but you will get stuff like that in the exam. Let's go through the maths of this question together. Step 1: E = ? k = 10 x = 0.09 Step 2: E = (0.5 x 10) x (0.09 x 0.09) Step 3: E = 5 x 0.0081 Step 4: E = 0.0405 J Then round to 2 decimal places: E = 0.04 J
• Question 9

A spring has an original length of 0.02 m and is stretched to a new length of 1.04 m. The spring has a spring constant of 30 N/m.

Calculate the energy stored by the spring.

Give you answer to 1 decimal place.

EDDIE SAYS
In this question, you had to find out the extension of the spring first because you were not given it in the question. It's simple, you just had to take the original length from the final length. Let's take a look at it: Step 1: E = ? k = 30 N/m x = 1.04 (final length) - 0.02 (original length) x = 1.02 m Step 2: E = (0.5 x 30) x (1.02 x 1.02) Step 3: E = 15 x 1.0404 E = 15.6 J 1 decimal place, remember?
• Question 10

A man falls 15 m in a bungee jump before the bungee becomes tight. He then moves a further 8 m, stretching the band. The bungee is quoted as having a spring constant of 60 N/m

Calculate the energy stored by the bungee.

EDDIE SAYS
In this one, there are some red herrings in the text to try and confuse you. Are you interested in how long the bungee is, or how much it extends when it is stretched? Just stretched, right? So, you need to ignore the first 15 m because the bungee is not even tight during this phase. So, how do we do it? Like this! E = ? k = 60 N/m x = 8 m E = (0.5 x 60) x (8 x 8) E = 30 x 64 E = 1,920 J Well done for completing another activity. Do you feel a bit more confident with using this equation now? 