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Hooke's Law and Basic Principles
Hooke's Law is your starting point for understanding material behaviour. It states that for elastic springs, extension is directly proportional to the applied force: F = kx. The spring constant (k) tells you how stiff the material is - higher values mean you need more force for the same stretch.
However, comparing different materials using just force and extension isn't fair since size matters. That's where stress and strain come in. Stress measures force per unit area, whilst strain measures extension relative to original length.
Young's modulus (E) is the golden ratio here - it's stress divided by strain when the material obeys Hooke's law. Two samples might have different spring constants, but if they're the same material, they'll have identical Young's modulus values.
Key insight: Young's modulus is like a material's fingerprint - it stays constant regardless of sample size.
Force-Extension Graphs and Material Categories
Force-extension graphs reveal a material's personality. The straight portion shows elastic behaviour - remove the force and the material springs back. Beyond point X, you enter plastic deformation where permanent changes occur and Hooke's law no longer applies.
The area under the graph represents work done. In the elastic region, this becomes elastic potential energy stored in the material. Once you exceed Hooke's law limits, that extra work goes into breaking bonds permanently.
Materials fall into three main categories. Crystalline materials (like metals) have ordered atomic structures making them ductile and tough. Amorphous materials (glass, ceramics) lack ordered structure and tend to be brittle. Polymeric materials contain long chain molecules with strong, flexible bonds.
Remember: The area under any force-extension graph always equals work done, even when Hooke's law doesn't apply.
Stress-Strain Graphs and Polymer Types
Stress-strain graphs are more useful than force-extension graphs because they let you compare different materials fairly. The gradient of the straight section gives you Young's modulus directly.
These graphs reveal key points: the limit of proportionality (where Hooke's law ends), the elastic limit, and the yield point (where massive strain occurs with little stress increase). Metals can deform extensively before breaking, absorbing loads of energy.
Thermoplastic polymers soften when heated and can be reshaped multiple times - think plastic bottles. Thermosetting polymers undergo permanent chemical changes when first heated and will crack or char if reheated - like the resin in fibreglass.
The breaking stress and yield stress values tell you how much punishment a material can take before failing permanently.
Pro tip: High Young's modulus means strong and stiff - metals typically score high on both strength and toughness.
Dislocations and Material Failure
Dislocations are tiny gaps in crystalline structures that act like weak spots, allowing atomic planes to slip more easily. Ironically, these defects make metals weaker but also more workable.
Engineers combat dislocations by adding foreign atoms to fill gaps or creating more grain boundaries to trap dislocations. When dislocations reach grain edges, they change the crystal's shape permanently.
Necking occurs during plastic deformation when a material's cross-sectional area reduces. This creates a weak point that needs less stress to continue extending, shown by the dip in stress-strain curves. Ductile fracture happens when necking continues until the material separates completely.
Different materials show varying degrees of ductility - from highly ductile (lots of plastic deformation) to brittle (immediate fracture with no plastic deformation).
Key concept: Dislocations make metals both weaker and more workable - it's all about controlling them effectively.
Brittle Materials and Rubber Behaviour
Brittle materials often have high Young's modulus (very strong) but low toughness - they don't absorb much energy before fracturing. They obey Hooke's law almost until they suddenly snap.
Crack propagation is the villain here. Small surface imperfections concentrate stress lines around crack tips, magnifying local stress and causing catastrophic failure. Without mobile dislocations to relieve stress, cracks just keep growing.
Smart engineering puts brittle materials under compression rather than tension. Pre-stressed concrete uses steel rods under tension, whilst pre-stressed glass cools rapidly so the surface sets under compression.
Rubber behaves uniquely with its low Young's modulus and hysteresis - different loading and unloading curves. When stretched, tangled polymer chains straighten out. The area between loading/unloading curves represents energy lost as heat.
Engineering insight: Work with brittle materials' strengths (compression) rather than against their weaknesses (tension) for safer structures.
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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
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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
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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
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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
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Sudenaz Ocak
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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
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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 Solids Under Stress in A-Level Physics
Ever wondered why some materials bounce back after being stretched whilst others snap or permanently bend? Understanding how solids behave under stress is crucial for everything from building bridges to designing your phone screen.
Hooke's Law and Basic Principles
Hooke's Law is your starting point for understanding material behaviour. It states that for elastic springs, extension is directly proportional to the applied force: F = kx. The spring constant (k) tells you how stiff the material is - higher values mean you need more force for the same stretch.
However, comparing different materials using just force and extension isn't fair since size matters. That's where stress and strain come in. Stress measures force per unit area, whilst strain measures extension relative to original length.
Young's modulus (E) is the golden ratio here - it's stress divided by strain when the material obeys Hooke's law. Two samples might have different spring constants, but if they're the same material, they'll have identical Young's modulus values.
Key insight: Young's modulus is like a material's fingerprint - it stays constant regardless of sample size.
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Force-Extension Graphs and Material Categories
Force-extension graphs reveal a material's personality. The straight portion shows elastic behaviour - remove the force and the material springs back. Beyond point X, you enter plastic deformation where permanent changes occur and Hooke's law no longer applies.
The area under the graph represents work done. In the elastic region, this becomes elastic potential energy stored in the material. Once you exceed Hooke's law limits, that extra work goes into breaking bonds permanently.
Materials fall into three main categories. Crystalline materials (like metals) have ordered atomic structures making them ductile and tough. Amorphous materials (glass, ceramics) lack ordered structure and tend to be brittle. Polymeric materials contain long chain molecules with strong, flexible bonds.
Remember: The area under any force-extension graph always equals work done, even when Hooke's law doesn't apply.
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Stress-Strain Graphs and Polymer Types
Stress-strain graphs are more useful than force-extension graphs because they let you compare different materials fairly. The gradient of the straight section gives you Young's modulus directly.
These graphs reveal key points: the limit of proportionality (where Hooke's law ends), the elastic limit, and the yield point (where massive strain occurs with little stress increase). Metals can deform extensively before breaking, absorbing loads of energy.
Thermoplastic polymers soften when heated and can be reshaped multiple times - think plastic bottles. Thermosetting polymers undergo permanent chemical changes when first heated and will crack or char if reheated - like the resin in fibreglass.
The breaking stress and yield stress values tell you how much punishment a material can take before failing permanently.
Pro tip: High Young's modulus means strong and stiff - metals typically score high on both strength and toughness.
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Dislocations and Material Failure
Dislocations are tiny gaps in crystalline structures that act like weak spots, allowing atomic planes to slip more easily. Ironically, these defects make metals weaker but also more workable.
Engineers combat dislocations by adding foreign atoms to fill gaps or creating more grain boundaries to trap dislocations. When dislocations reach grain edges, they change the crystal's shape permanently.
Necking occurs during plastic deformation when a material's cross-sectional area reduces. This creates a weak point that needs less stress to continue extending, shown by the dip in stress-strain curves. Ductile fracture happens when necking continues until the material separates completely.
Different materials show varying degrees of ductility - from highly ductile (lots of plastic deformation) to brittle (immediate fracture with no plastic deformation).
Key concept: Dislocations make metals both weaker and more workable - it's all about controlling them effectively.
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Brittle Materials and Rubber Behaviour
Brittle materials often have high Young's modulus (very strong) but low toughness - they don't absorb much energy before fracturing. They obey Hooke's law almost until they suddenly snap.
Crack propagation is the villain here. Small surface imperfections concentrate stress lines around crack tips, magnifying local stress and causing catastrophic failure. Without mobile dislocations to relieve stress, cracks just keep growing.
Smart engineering puts brittle materials under compression rather than tension. Pre-stressed concrete uses steel rods under tension, whilst pre-stressed glass cools rapidly so the surface sets under compression.
Rubber behaves uniquely with its low Young's modulus and hysteresis - different loading and unloading curves. When stretched, tangled polymer chains straighten out. The area between loading/unloading curves represents energy lost as heat.
Engineering insight: Work with brittle materials' strengths (compression) rather than against their weaknesses (tension) for safer structures.
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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 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