Force and extension Revision Notes for AQA GCSE Physics Combined Science

Force and extension

What happens when forces act on springs

When you apply a force to a spring, it changes shape. This is called elastic distortion. The spring stretches or compresses, but it can return to its original shape when you remove the force.

infoNote

The spring stores energy when it's stretched or compressed. This stored energy can be released when the force is removed, allowing the spring to return to its original shape.

Hooke's law

For springs that behave elastically, there's a simple relationship between the force applied and how much the spring extends. This fundamental principle governs how springs work in countless applications, from car suspensions to measuring devices.

chatImportant

Hooke's Law: Force is directly proportional to extension (up to a certain limit)

The equation is:

$F = ke$

Where:

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

What is spring constant?

The spring constant tells you how stiff a spring is. This value is unique to each spring and depends on the material and construction:

infoNote

Higher spring constant = stiffer spring (harder to stretch)
Lower spring constant = easier to stretch

Think of it as the spring's "personality" - some springs are naturally more resistant to being stretched than others.

What is extension?

Extension is how much longer the spring gets when stretched. It's crucial to understand that extension is not the total length of the spring:

Extension = total stretched length - original length

Elastic potential energy

When you stretch a spring, you do work on it. This energy gets stored as elastic potential energy. The energy stored depends on both how stiff the spring is and how much you've stretched it.

The equation is:

$E_p = \frac{1}{2}ke^2$

Where:

$E_p$ = elastic potential energy (in Joules, J)
k = spring constant (in N/m)
e = extension (in metres, m)

chatImportant

The work you do stretching the spring equals the elastic potential energy stored. This is a direct application of the conservation of energy principle.

Force-extension graphs

A force-extension graph shows how force and extension are related. These graphs provide valuable information about spring behaviour and help us understand the limits of Hooke's law.

infoNote

Key features of force-extension graphs:

Straight line section: Shows elastic behaviour - the spring follows Hooke's law
Gradient of the line: Equals the spring constant (k)
Curved section: Shows the limit of proportionality has been exceeded
Area under the graph: Shows the energy stored in the spring

Reading the graph

While the line is straight, force and extension are proportional. When the line curves, the spring is no longer behaving elastically and has exceeded its limit of proportionality.

Working with calculations

Understanding how to manipulate the equations is essential for solving spring problems effectively.

lightbulbExample

Worked Example: Spring Calculations

Finding spring constant: Use $k = \frac{F}{e}$

Finding extension: Use $e = \frac{F}{k}$

Finding energy stored: Use $E_p = \frac{1}{2}ke^2$

Step-by-step approach:

Identify what you're looking for
Choose the correct equation
Substitute known values
Check your units are correct

infoNote

Important units to remember:

Force: Newtons (N)
Extension: metres (m)
Spring constant: N/m
Energy: Joules (J)

Top tip: Always convert measurements to the correct units before calculating!

bookmarkSummary

Key Points to Remember:

Hooke's Law: $F = ke$ (force equals spring constant times extension)
Energy stored: $E_p = \frac{1}{2}ke^2$ (half times spring constant times extension squared)
Spring constant shows how stiff a spring is - higher values mean stiffer springs
Extension is the extra length when stretched, not the total length
Force-extension graphs have a straight line section where the spring behaves elastically

Force and extension (AQA GCSE Physics Combined Science): Revision Notes