Force and extension Revision Notes for AQA GCSE Physics

Force and extension

What happens when you stretch a spring?

When you apply a force to a spring, it stretches. This stretching is called elastic distortion. The spring stores energy as it gets longer.

The key thing to remember is that for most springs, there's a direct relationship between the force you apply and how much the spring stretches.

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When a spring stores energy during stretching, this energy can be released when the spring returns to its original shape. This is why springs are useful in many mechanical devices.

Hooke's law

Hooke's law tells us exactly how force and extension are linked:

$F = ke$

Where:

F = force applied (in Newtons, N)
k = spring constant (in N/m)
e = extension (in metres, m)

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The spring constant tells you how stiff the spring is. A higher spring constant means a stiffer spring that's harder to stretch. This value is unique to each spring and remains constant as long as the spring follows Hooke's law.

Working out the extension

Extension means how much longer the spring gets:

Extension = total stretched length - original length

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Worked Example: Calculating Extension

If a spring starts at 10cm and stretches to 15cm, the extension is: Extension = 15cm - 10cm = 5cm

Energy stored in springs

When you stretch a spring, you do work on it. This work gets stored as elastic potential energy.

The formula is: $E_s = \frac{1}{2}ke^2$

Where $E_s$ is the elastic potential energy stored (in Joules, J).

Force-extension graphs

These graphs show how force and extension are related:

The straight line shows the spring following Hooke's law
The gradient (slope) of the line gives you the spring constant
The area under the line tells you the energy stored in the spring
Beyond the limit of proportionality, the spring stops following Hooke's law

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The straight-line relationship on a force-extension graph is the visual representation of Hooke's law. When this line becomes curved, it indicates the spring is being stretched beyond its elastic limit.

Calculating spring constants

To find the spring constant, rearrange $F = ke$ :

$k = \frac{F}{e}$

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Worked Example: Finding Spring Constant

If 12N stretches a spring by 0.25m: $k = \frac{12N}{0.25m} = 48N/m$

Working out energy stored

You can calculate the energy stored in two ways:

Using $E_s = \frac{1}{2}ke^2$
Using the area under a force-extension graph = $\frac{1}{2} \times \text{force} \times \text{extension}$

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Both methods will give you the same answer when the spring follows Hooke's law. The area under the graph method is particularly useful when you have experimental data plotted on a graph.

Important tips for calculations

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Common Mistakes to Avoid:

Always use Newtons for force
Always use metres for extension and length
The extension is what matters, not the total length
Check your units are correct before calculating

Remember!

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Key Points to Remember:

Force and extension are directly proportional ( $F = ke$ ) up to the limit of proportionality
Spring constant tells you how stiff a spring is - higher values mean stiffer springs
Energy stored in a spring = $\frac{1}{2}ke^2$
Force-extension graphs have a straight line when following Hooke's law
The area under the graph gives you the energy stored in the spring

Force and extension (AQA GCSE Physics): Revision Notes