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23 Dec 2025
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Understanding Elastic Potential Energy for GCSE Students
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Understanding Elastic Potential Energy
When you pull back a catapult or bounce on a trampoline, you're storing elastic potential energy. This happens whenever you stretch or compress something springy like a spring, rubber band, or bungee cord.
The amount of energy stored depends on two key factors: how much you extend the material (the change in length, not the total length) and the spring constant (how stiff the material is). A stiffer spring needs more force to stretch the same distance, so it stores more energy.
Think of it like this: stretching a thick rubber band 5cm takes way more effort than stretching a thin one the same distance. The thick band has a higher spring constant and will store more energy.
Quick Tip: Extension is just the change in length - whether something gets longer or shorter and by how much!
The EPE Formula You Need to Know
The formula for elastic potential energy is: EPE = ½ × k × e². Don't worry about memorising it - you'll get this formula in your exam! Here's what each bit means: EPE is in joules (J), k is the spring constant in N/m, and e is the extension in metres.
Notice that extension is squared in the formula. This means doubling the stretch gives you four times more stored energy - pretty powerful stuff! Always remember to convert units properly: centimetres to metres, and kilojoules to joules.
For bungee jumping, you'd want a rope with a low spring constant. A high spring constant would barely stretch, causing a painful sudden stop instead of a smooth bounce.
Exam Success: This formula works for both stretching and compressing - the physics is exactly the same!
Calculating Elastic Potential Energy
Let's work through some typical calculations you'll see in exams. If a spring has k = 20 N/m and extends by 0.15m, then EPE = ½ × 20 × (0.15)² = 0.225J. Remember to square the extension first, then multiply by everything else.
Car suspension springs are a great real-world example. With k = 64,000 N/m compressed by 4cm (0.04m), each spring stores EPE = ½ × 64,000 × (0.04)² = 51.2J when hitting a bump.
Always watch your unit conversions: 20cm becomes 0.2m, and 64kN/m becomes 64,000 N/m. Getting the units wrong will mess up your entire calculation, even if your method is perfect.
Pro Tip: Write down your unit conversions first - it saves marks and prevents silly mistakes!
Finding Spring Constants
Sometimes you'll need to work backwards from the EPE formula to find the spring constant. Start with EPE = ½ke², then rearrange to get k = 2EPE/e². It's just algebra - you've got this!
For example, if EPE = 5J and extension = 0.2m, then k = (2 × 5)/(0.2)² = 10/0.04 = 250 N/m. The key is being systematic: substitute your values, then calculate step by step.
Real springs can have massive spring constants. A spring storing 2.5kJ when compressed by just 25mm has k = 8,000,000 N/m - that's seriously stiff! These calculations show why car parts need to be so robust.
Method Reminder: Always substitute numbers into the rearranged formula before doing any calculations - it keeps everything clear!
Calculating Extension
To find extension, rearrange the formula to get e = √. Don't forget the square root - it's easy to miss but absolutely essential for getting the right answer.
If a spring with k = 160 N/m stores 40J, then e = √(2 × 40/160) = √0.5 = 0.707m. Some answers will be nice round numbers, but many will need your calculator's square root function.
Large-scale examples can be mind-blowing: a spring storing 42MJ with k = 25kN/m extends by 58 metres! These massive numbers show up in industrial applications like bridge shock absorbers.
Calculator Tip: Double-check your square root calculations - they're the most common place to make errors in EPE problems!
Energy Transfers and Conservation
Here's where elastic potential energy gets really exciting - it can transform into other energy types! When a catapult launches a ball, EPE converts to kinetic energy. When the ball reaches maximum height, that kinetic energy becomes gravitational potential energy.
For a 1.5kg ball launched by a spring , the EPE = 250J becomes kinetic energy, giving initial velocity v = 18.3 m/s. This same energy then becomes gravitational potential energy, lifting the ball to 16.7m high.
The beauty of energy conservation means these calculations connect perfectly. The EPE at the start equals the GPE at the top - energy transforms but never disappears.
Key Insight: Energy conservation problems often involve EPE → KE → GPE transformations - learn this pattern!
Exam-Style Applications
Bungee jumping problems combine all your EPE knowledge with real-world physics. When a 50kg student falls 20m, their gravitational potential energy converts to kinetic energy (with some energy lost to air resistance).
The key is tracking energy step-by-step: calculate the GPE lost during the fall, work out how much becomes kinetic energy, then find the speed. Finally, when the bungee cord stretches, kinetic energy transforms back into elastic potential energy.
For a bungee cord that stretches 35m and stores 24.5kJ, you can calculate its spring constant: k = 40 N/m. These multi-step problems test everything you've learned about energy transfers.
Exam Strategy: Break complex problems into smaller steps - GPE first, then KE, then EPE. Take it one energy type at a time!
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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
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Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Understanding Elastic Potential Energy for GCSE Students
Ever wondered how trampolines, bungee cords, and car suspension work? They all rely on elastic potential energy- the energy stored when you stretch or compress springy materials. Understanding this concept will help you tackle physics problems and see the... Show more
Understanding Elastic Potential Energy
When you pull back a catapult or bounce on a trampoline, you're storing elastic potential energy. This happens whenever you stretch or compress something springy like a spring, rubber band, or bungee cord.
The amount of energy stored depends on two key factors: how much you extend the material (the change in length, not the total length) and the spring constant (how stiff the material is). A stiffer spring needs more force to stretch the same distance, so it stores more energy.
Think of it like this: stretching a thick rubber band 5cm takes way more effort than stretching a thin one the same distance. The thick band has a higher spring constant and will store more energy.
Quick Tip: Extension is just the change in length - whether something gets longer or shorter and by how much!
Sign up to see the contentIt's free!
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Join milions of students
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The EPE Formula You Need to Know
The formula for elastic potential energy is: EPE = ½ × k × e². Don't worry about memorising it - you'll get this formula in your exam! Here's what each bit means: EPE is in joules (J), k is the spring constant in N/m, and e is the extension in metres.
Notice that extension is squared in the formula. This means doubling the stretch gives you four times more stored energy - pretty powerful stuff! Always remember to convert units properly: centimetres to metres, and kilojoules to joules.
For bungee jumping, you'd want a rope with a low spring constant. A high spring constant would barely stretch, causing a painful sudden stop instead of a smooth bounce.
Exam Success: This formula works for both stretching and compressing - the physics is exactly the same!
Sign up to see the contentIt's free!
Access to all documents
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Join milions of students
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Calculating Elastic Potential Energy
Let's work through some typical calculations you'll see in exams. If a spring has k = 20 N/m and extends by 0.15m, then EPE = ½ × 20 × (0.15)² = 0.225J. Remember to square the extension first, then multiply by everything else.
Car suspension springs are a great real-world example. With k = 64,000 N/m compressed by 4cm (0.04m), each spring stores EPE = ½ × 64,000 × (0.04)² = 51.2J when hitting a bump.
Always watch your unit conversions: 20cm becomes 0.2m, and 64kN/m becomes 64,000 N/m. Getting the units wrong will mess up your entire calculation, even if your method is perfect.
Pro Tip: Write down your unit conversions first - it saves marks and prevents silly mistakes!
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Finding Spring Constants
Sometimes you'll need to work backwards from the EPE formula to find the spring constant. Start with EPE = ½ke², then rearrange to get k = 2EPE/e². It's just algebra - you've got this!
For example, if EPE = 5J and extension = 0.2m, then k = (2 × 5)/(0.2)² = 10/0.04 = 250 N/m. The key is being systematic: substitute your values, then calculate step by step.
Real springs can have massive spring constants. A spring storing 2.5kJ when compressed by just 25mm has k = 8,000,000 N/m - that's seriously stiff! These calculations show why car parts need to be so robust.
Method Reminder: Always substitute numbers into the rearranged formula before doing any calculations - it keeps everything clear!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Calculating Extension
To find extension, rearrange the formula to get e = √. Don't forget the square root - it's easy to miss but absolutely essential for getting the right answer.
If a spring with k = 160 N/m stores 40J, then e = √(2 × 40/160) = √0.5 = 0.707m. Some answers will be nice round numbers, but many will need your calculator's square root function.
Large-scale examples can be mind-blowing: a spring storing 42MJ with k = 25kN/m extends by 58 metres! These massive numbers show up in industrial applications like bridge shock absorbers.
Calculator Tip: Double-check your square root calculations - they're the most common place to make errors in EPE problems!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
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Energy Transfers and Conservation
Here's where elastic potential energy gets really exciting - it can transform into other energy types! When a catapult launches a ball, EPE converts to kinetic energy. When the ball reaches maximum height, that kinetic energy becomes gravitational potential energy.
For a 1.5kg ball launched by a spring , the EPE = 250J becomes kinetic energy, giving initial velocity v = 18.3 m/s. This same energy then becomes gravitational potential energy, lifting the ball to 16.7m high.
The beauty of energy conservation means these calculations connect perfectly. The EPE at the start equals the GPE at the top - energy transforms but never disappears.
Key Insight: Energy conservation problems often involve EPE → KE → GPE transformations - learn this pattern!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Exam-Style Applications
Bungee jumping problems combine all your EPE knowledge with real-world physics. When a 50kg student falls 20m, their gravitational potential energy converts to kinetic energy (with some energy lost to air resistance).
The key is tracking energy step-by-step: calculate the GPE lost during the fall, work out how much becomes kinetic energy, then find the speed. Finally, when the bungee cord stretches, kinetic energy transforms back into elastic potential energy.
For a bungee cord that stretches 35m and stores 24.5kJ, you can calculate its spring constant: k = 40 N/m. These multi-step problems test everything you've learned about energy transfers.
Exam Strategy: Break complex problems into smaller steps - GPE first, then KE, then EPE. Take it one energy type at a time!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
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Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content: Elastic Potential Energy
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user