 # Understanding Elastic Energy

In this worksheet, students will look at how energy can be stored elastically and how to work out this 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

Difficulty level:   ### QUESTION 1 of 10

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 (0.0052)

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!

A person is stretching an elastic band. Name the correct input energy.

Kinetic

Elasitc

Gravitaitonal

Light

Heat

Match the units to the measurements below.

## Column B

Energy (E)
Joule (J)
Spring Constant (K)
Newton per meter (N/m)
Extention (x)
Meter (m)

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 is seeing happen.

Plastic limit

Elastic limit

Spring limit

Limit of tention

Sian pulls an elastic band 0.5 m. The elastic band has a spring constant of 30 N/m. Calculate the energy that Sian put into the stretching of the elastic band.

A car sits on springs that are used for suspension. When the car runs over a bump in the road, the springs compress by 0.05m. Calculate the energy that went into the individual spring in the car wheels. Include the units in your answer.

Mass of car = 1500 kg

Spring constant of springs = 3000 N/m

A weighbridge is a device that s used to find out the mass of a large vehicle like a lorry. It works by having a large metal plate sit on 4 springs, then 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 into the whole bridge.

What type of energy is being stored by the 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. Give your answers to 2 decimal places.

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 one decimal place

A man falls in a bungee jump 15 m 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 correct input energy.

Kinetic
EDDIE SAYS
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! Just think of the Kinect for the X-Box (too old school? It might be too old school...)
• Question 2

Match the units to the measurements below.

## Column B

Energy (E)
Joule (J)
Spring Constant (K)
Newton per meter (N/m)
Extention (x)
Meter (m)
EDDIE SAYS
If you ever get stuck with these, think about what would make sense and work your way backward. Extention is a measurement of distance - we also measure distance in meters so extension must be in meters, right? Good! Next, Energy can be measured with a joulemeter, so it must have something to do with a Joule? Yes! Finally, then one that is left must be the spring constant. DONE!
• 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 is seeing 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. So 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 everything else! Now only the first three remain! How are we going to limit them down? Plastic isn't elastic (it technically means the opposite) and then we are left with two. So now it's a 50/50 guess, or you could trust us 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 put into the stretching of the elastic band.

3.75
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 1000 times until how to answer the question is firmly fixed into your head. Find the numbers and write them down: E = ? k = 30 N/m x = 0.5 m Put them into the equation: 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 DONE!
• 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 0.05m. Calculate the energy that went into the individual spring in the car wheels. Include the units in your answer.

Mass of car = 1500 kg

Spring constant of springs = 3000 N/m

3.75J
3.75 J
EDDIE SAYS
Did you remember to include the unit? You need to read the whole questions and (in the real paper) underline the things that you think will get you the marks. So, how do we answer this question? It's simple if you follow the steps! It's almost like we're given you a set of tools to help you to be successful in exams or something... Step one - 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! We're so nice to you :) Step 2 - Put the numbers into the equation. E = (0.5 x 3000) x (0.05 x 0.05) Step 3 - so the stuff in the brackets: E = 1500 x 0.0025 Step 4 - finish off with the maths! E = 3.75 J Don't forget the unit!
• Question 6

A weighbridge is a device that s used to find out the mass of a large vehicle like a lorry. It works by having a large metal plate sit on 4 springs, then 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 into the whole bridge.

4400
4,400
EDDIE SAYS
This one is a little more complex - there are 4 springs, so we need to multiply whatever answer we get with 4 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 answer this question. 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 4 to get the total for all of the springs. 1,100 x 4 = 4,400 J DONE!
• Question 7

What type of energy is being stored by the 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. Give your answers to 2 decimal places.

0.04
EDDIE SAYS
Did you remember to put your answer to 2 decimal places? Well done if you did! We totally put it in there to trip you up, but you will get stuff like that in an 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 = 10 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 one decimal place

15.6
EDDIE SAYS
In this question, you had to find out the extension of the spring 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 how we would have done 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 One decimal place, remember? DONE! yay
• Question 10

A man falls in a bungee jump 15 m 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.

1920
1,920
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 want 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 DONE! 