Hooke's Law and Elasticity in Physics: Understanding force-extension relationships... Show more
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Updated Mar 23, 2026
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Fun with Hooke's Law and Springy Science: Force-Extension Graphs and More
Reuben Cowell
@reubencowell
1 / 5
Elastic and Inelastic Deformation
Objects can undergo either elastic or inelastic deformation when subjected to forces.
Definition: Elastic deformation occurs when an object returns to its original shape after the applied force is removed.
Definition: Inelastic deformation occurs when an object does not fully return to its original shape after the applied force is removed.
Examples of elastic objects:
- Springs
- Elastic bands
Examples of inelastic objects:
- Plastic
- Clay
Highlight: The elastic and inelastic deformation in physics concept is crucial for understanding material properties and behavior under stress.
Work Done on a Spring
When a spring is stretched or compressed, work is done, and energy is transferred to its elastic potential energy store. The work done on a spring can be calculated using the equation:
Formula: Ee = ½ × k × x²
Where:
- Ee is the elastic potential energy
- k is the spring constant
- x is the extension
Highlight: This formula only applies to objects that haven't exceeded their limit of proportionality.
Hooke's Law and Extension
Hooke's law is a fundamental principle in physics that describes the relationship between force and extension in elastic objects.
Definition: Hooke's law states that the extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality.
The limit of proportionality is the point beyond which an elastic object may extend but won't return to its original shape when the force is removed. This value varies by material.
Force-Extension Graphs
Force-extension graphs visually represent Hooke's law. These graphs typically show:
- A linear region where force and extension are directly proportional
- A non-linear region beyond the limit of proportionality (marked as point P)
Example: In a force-extension graph for a spring, the initial straight line represents the elastic region, while the curved portion indicates the plastic region.
Calculating Spring Constant
The spring constant (k) can be determined from force-extension graphs by finding the gradient:
Formula: k = gradient = ΔF / Δe
Where:
- ΔF is the change in force
- Δe is the change in extension
Highlight: A steeper gradient indicates a larger spring constant, meaning the spring is stiffer.
Using Hooke's Law
Hooke's Law is expressed by the equation:
Formula: F = k × e
Where:
- F is the force (in Newtons, N)
- k is the spring constant
- e is the extension (in meters, m)
Vocabulary: Extension is calculated by subtracting the original length from the final length of the object.
Solving Hooke's Law Problems
To solve problems using Hooke's Law:
- List known quantities
- Write down and rearrange the relevant equation
- Calculate extension
- Convert units if necessary
- Substitute values into the equation
Highlight: Pay attention to units when solving Hooke's Law problems. The standard units are meters for length and Newtons per meter for spring constant.
Example: When calculating the spring constant using force extension graphs, ensure that you convert centimeters to meters by dividing by 100.
This comprehensive guide provides a solid foundation for understanding Hooke's law force extension relationship and related concepts in physics, suitable for GCSE and KS3 level students.
Answering Hooke's Law Questions
This page provides a step-by-step guide on how to approach and solve problems related to Hooke's Law.
Steps to answer a Hooke's Law question:
- List known quantities
- Write down and rearrange the relevant equation
- Calculate extension
- Convert units if necessary
- Substitute values into the equation
Highlight: Pay close attention to units when solving Hooke's Law problems. Most springs are measured in centimeters, but Hooke's Law uses meters, so conversion may be necessary.
Example: The page includes a visual representation of a spring, highlighting the original length, final length, and the force (weight) applied, to help students understand how to apply Hooke's Law in practical scenarios.
Changing Shape and Deformation
When multiple forces act on an object, it may undergo deformation through stretching, compressing, or bending. This process transfers energy to the object's elastic potential energy store.
Definition: Deformation refers to a change in an object's shape due to applied forces.
The three main types of deformation are:
- Stretching: Forces acting in opposite directions away from the object
- Compressing: Forces acting in opposite directions towards the object
- Bending: Forces distorting the object's shape
Highlight: Deformation only occurs when two or more forces are applied. A single force would simply cause the object to move.
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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 Knowunity AI. 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
Fun with Hooke's Law and Springy Science: Force-Extension Graphs and More
Reuben Cowell
@reubencowell
Hooke's Law and Elasticity in Physics: Understanding force-extension relationships and deformation
- Explores the principles of Hooke's law force-extension relationship and its applications in physics
- Covers elastic and inelastic deformation in physics, including stretching, compressing, and bending of objects... Show more
Elastic and Inelastic Deformation
Objects can undergo either elastic or inelastic deformation when subjected to forces.
Definition: Elastic deformation occurs when an object returns to its original shape after the applied force is removed.
Definition: Inelastic deformation occurs when an object does not fully return to its original shape after the applied force is removed.
Examples of elastic objects:
- Springs
- Elastic bands
Examples of inelastic objects:
- Plastic
- Clay
Highlight: The elastic and inelastic deformation in physics concept is crucial for understanding material properties and behavior under stress.
Work Done on a Spring
When a spring is stretched or compressed, work is done, and energy is transferred to its elastic potential energy store. The work done on a spring can be calculated using the equation:
Formula: Ee = ½ × k × x²
Where:
- Ee is the elastic potential energy
- k is the spring constant
- x is the extension
Highlight: This formula only applies to objects that haven't exceeded their limit of proportionality.
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Hooke's Law and Extension
Hooke's law is a fundamental principle in physics that describes the relationship between force and extension in elastic objects.
Definition: Hooke's law states that the extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality.
The limit of proportionality is the point beyond which an elastic object may extend but won't return to its original shape when the force is removed. This value varies by material.
Force-Extension Graphs
Force-extension graphs visually represent Hooke's law. These graphs typically show:
- A linear region where force and extension are directly proportional
- A non-linear region beyond the limit of proportionality (marked as point P)
Example: In a force-extension graph for a spring, the initial straight line represents the elastic region, while the curved portion indicates the plastic region.
Calculating Spring Constant
The spring constant (k) can be determined from force-extension graphs by finding the gradient:
Formula: k = gradient = ΔF / Δe
Where:
- ΔF is the change in force
- Δe is the change in extension
Highlight: A steeper gradient indicates a larger spring constant, meaning the spring is stiffer.
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Using Hooke's Law
Hooke's Law is expressed by the equation:
Formula: F = k × e
Where:
- F is the force (in Newtons, N)
- k is the spring constant
- e is the extension (in meters, m)
Vocabulary: Extension is calculated by subtracting the original length from the final length of the object.
Solving Hooke's Law Problems
To solve problems using Hooke's Law:
- List known quantities
- Write down and rearrange the relevant equation
- Calculate extension
- Convert units if necessary
- Substitute values into the equation
Highlight: Pay attention to units when solving Hooke's Law problems. The standard units are meters for length and Newtons per meter for spring constant.
Example: When calculating the spring constant using force extension graphs, ensure that you convert centimeters to meters by dividing by 100.
This comprehensive guide provides a solid foundation for understanding Hooke's law force extension relationship and related concepts in physics, suitable for GCSE and KS3 level students.
Sign up to see the contentIt's free!
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Answering Hooke's Law Questions
This page provides a step-by-step guide on how to approach and solve problems related to Hooke's Law.
Steps to answer a Hooke's Law question:
- List known quantities
- Write down and rearrange the relevant equation
- Calculate extension
- Convert units if necessary
- Substitute values into the equation
Highlight: Pay close attention to units when solving Hooke's Law problems. Most springs are measured in centimeters, but Hooke's Law uses meters, so conversion may be necessary.
Example: The page includes a visual representation of a spring, highlighting the original length, final length, and the force (weight) applied, to help students understand how to apply Hooke's Law in practical scenarios.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Changing Shape and Deformation
When multiple forces act on an object, it may undergo deformation through stretching, compressing, or bending. This process transfers energy to the object's elastic potential energy store.
Definition: Deformation refers to a change in an object's shape due to applied forces.
The three main types of deformation are:
- Stretching: Forces acting in opposite directions away from the object
- Compressing: Forces acting in opposite directions towards the object
- Bending: Forces distorting the object's shape
Highlight: Deformation only occurs when two or more forces are applied. A single force would simply cause the object to move.
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?
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Is Knowunity really free of charge?
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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 Knowunity AI. 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 Knowunity AI. 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