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A force-extension graph is a straight line through the origin while Hooke's Law applies, and its gradient is the spring constant. Free GCSE Physics notes.
Elasticity Explained: Forces, Deformation and Springs is part of Forces and elasticity in GCSE AQA Higher Physics.
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A force-extension graph is a straight line through the origin while Hooke's Law applies, and its gradient is the spring constant. Free GCSE Physics notes.
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Use this lesson to stay inside Forces and elasticity while connecting the detail back to the wider Forces topic.
Read the core explanations from Elasticity Explained: Forces, Deformation and Springs before testing yourself from memory.
Picture trying to stretch a rubber band with just one finger. Nothing happens, right? You need to pull from both ends to make it longer.
This reveals a fundamental truth about deformation: changing an object's shape always requires at least two forces acting in different directions. One force alone can only accelerate an object - it cannot deform it.
When you stretch a spring, one end is pulled while the other end is held or pulled the other way. When you compress a sponge, your hand pushes down while the table pushes up. These forces act on different parts of the object and are often equal in size and opposite in direction. That pair of forces can deform the object even when the overall forces balance.
Common examples include stretching a guitar string (tension forces at both ends), bending a ruler (forces creating a turning moment), and compressing a car suspension spring (weight pushing down, road pushing up). In each case, multiple forces work together to change the object's shape.
Not all deformations are created equal. Some materials bounce back to their original shape like a spring, whilst others stay permanently changed like plasticine.
Think of a rubber band versus a piece of chewing gum. Stretch the rubber band and let go - it snaps back to its original length. This is elastic deformation. Stretch the chewing gum and let go - it stays longer. This is inelastic deformation.
The key difference lies in what happens to the energy you put in. During elastic deformation, your energy gets stored as elastic potential energy and can be recovered. During inelastic deformation, your energy gets converted to heat and sound - it's lost forever.
Materials behave elastically up to the elastic limit, which means they return to their original shape when the force is removed. The limit of proportionality is slightly different: it is the point up to which force is directly proportional to extension. A spring can stop obeying Hooke’s law before it reaches the elastic limit.
Robert Hooke discovered something remarkable about springs in 1676: double the force, double the extension. Triple the force, triple the extension. This beautifully simple relationship is called Hooke's Law.
This creates a linear relationship - if you plot force against extension, you get a straight line through the origin. The gradient of this line is the spring constant, which tells you how stiff the spring is.
A stiff spring (high k value) needs a large force to produce a small extension. A soft spring (low k value) extends easily with small forces. The spring constant is like the spring's 'personality' - it never changes for a particular spring.
Hooke’s law applies only up to the limit of proportionality, where force and extension are in a straight-line relationship. Beyond that point, the graph curves. The object may still return to its original shape for a while, but the force is no longer directly proportional to the extension or compression.
Hooke's Law calculations are common in exams, but there's a trap many students fall into. Let's work through some examples to avoid the pitfalls.
Worked example: Finding Spring Constant
A spring extends by 8.0 cm when a 12 N force is applied. Calculate the spring constant. [3 marks]
Answer: 150 N/m
The most common mistake in these calculations is forgetting to convert centimetres to metres. Always check your units before substituting into the formula.
Worked example: Finding Extension
A spring with spring constant 250 N/m has a 15 N force applied. Calculate the extension. [2 marks]
Answer: 0.060 m or 6.0 cm
When you stretch a spring, where does your energy go? It doesn't disappear - it gets stored as elastic potential energy, ready to be released when the spring returns to its original length.
Think of a catapult or a bow and arrow. You do work stretching the elastic material, storing energy. When you release it, this stored energy converts to kinetic energy, launching the projectile.
Notice that energy depends on the square of the extension. Double the extension, and you store four times the energy. This is why it gets progressively harder to stretch a spring further.
The work done stretching the spring equals the elastic potential energy stored, provided the spring isn't damaged. This is a perfect example of energy conservation - no energy is lost in ideal elastic deformation.
Worked example: Calculating Elastic Potential Energy
A spring with spring constant 200 N/m is compressed by 5.0 cm. Calculate the elastic potential energy stored. [3 marks]
Answer: 0.25 J
Elasticity questions follow predictable patterns in exams. Master these techniques and you'll spot the traps before they catch you.
The biggest mistake students make is unit conversion. Springs extend by centimetres in real life, but physics equations need metres. Always convert before substituting - it's worth checking twice.
For 'describe' questions about deformation, examiners want you to mention that multiple forces are needed. Don't just say 'force is applied' - specify that forces act in different directions.
When explaining elastic versus inelastic deformation, the key word is 'returns'. Elastic materials return to original shape; inelastic materials don't. This simple distinction wins marks.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
A force-extension graph is a straight line through the origin while Hooke's Law applies, showing a linear relationship, and its gradient is the spring constant. Past the limit of proportionality the graph curves, so force is no longer directly proportional to extension.
In elastic deformation the object returns to its original shape when the forces are removed, and energy is stored. In inelastic deformation the change is permanent and energy is dissipated; a rubber band snaps back, but chewing gum stays longer.
Deformation is a change in the shape or size of an object caused by applied forces. The object may stretch, compress, bend or twist, as when stretching a guitar string, bending a ruler or compressing a car suspension spring.
A catapult and a bow and arrow both use elastic potential energy. Work is done stretching the elastic material, storing energy, and on release this stored energy converts to kinetic energy, launching the projectile.
Hooke's Law states that the extension of an elastic object is directly proportional to the applied force, provided the limit of proportionality is not exceeded: F = ke, where k is the spring constant. Double the force gives double the extension.
Changing an object's shape needs at least two forces acting in different directions, because one force alone can only accelerate an object. To stretch a spring, one end is pulled while the other is held; to compress a sponge, a hand pushes down while the table pushes up.
Rearrange Hooke's Law to e = F ÷ k. A spring with a spring constant of 250 N/m and a 15 N force applied has an extension of 15 ÷ 250 = 0.060 m, which is 6.0 cm.
A spring with a spring constant of 250 N/m and a 15 N force applied extends by 0.060 m, or 6.0 cm. Rearranging Hooke's law F = ke gives e = F ÷ k = 15 ÷ 250 = 0.060 m.
In inelastic deformation, the energy put in is converted to heat and sound and dissipated rather than stored. In elastic deformation, the energy is stored as elastic potential energy and can be recovered.
A rubber band shows elastic deformation, because it snaps back to its original length when let go. Chewing gum shows inelastic deformation, because it stays longer after being stretched.
Robert Hooke discovered in 1676 that doubling the force on a spring doubles the extension, and tripling the force triples it. This relationship, F = ke, is called Hooke's law.
A linear force-extension graph is a straight line through the origin, showing force directly proportional to extension, up to the limit of proportionality. Beyond that point the graph curves, so the relationship becomes non-linear even if the object still returns to its original shape.
A spring gets progressively harder to stretch further because the stored elastic potential energy depends on the square of the extension. Doubling the extension stores four times the energy, so more work is needed for each extra stretch.
The gradient of the straight-line part of a force-extension graph is the spring constant, showing how stiff the spring is. A stiff spring has a high k and needs a large force for a small extension, while a soft spring extends easily.