Forces
This lesson builds hooke's law, spring constant and elastic energy for GCSE Physics.
Use the core lesson first, then match the exam-board guidance to your school route. Many pupils meet this content through Combined Science as well as Separate Physics.
What you will learn
Exam-board fit
Exact paper labels and specification-point numbering vary by board and cohort, so match this lesson to your school route before using past-paper questions.
Spring practical data supplied on this page
Use the spring and rubber band examples to practise gradients, proportionality and elastic energy calculations.
Clear explanation
Hooke's law says force is proportional to extension until the limit of proportionality is reached. On a force-extension graph, this is the straight-line region through the origin.
The spring constant tells you how stiff a spring is. A larger spring constant means more force is needed for the same extension.
Elastic deformation is reversible when the force is removed. Inelastic deformation leaves the object permanently changed.
Key graph
Worked examples
Spring constant
A force of 12 N produces an extension of 0.04 m.
force = spring constant x extension
spring constant = force ÷ extension = 12 ÷ 0.04
Quick checks
Choose an answer, then check your thinking.
1. What does the straight-line part of a force-extension graph show?
2. What does a larger spring constant mean?
Practice questions
Question 1
A spring has k = 200 N/m and extension 0.03 m. Calculate force.
Reveal answer and marking guidance
Answer: 6 N.
Marking: Credit F = k x e and 200 x 0.03 = 6 N.
Question 2
A 5 N force extends a spring by 0.02 m. Calculate spring constant.
Reveal answer and marking guidance
Answer: 250 N/m.
Marking: Credit k = F ÷ e and 5 ÷ 0.02 = 250 N/m.
Question 3
What is meant by elastic deformation?
Reveal answer and marking guidance
Answer: The object returns to its original shape when the force is removed.
Marking: Credit reversible deformation.
Question 4
How can you identify the limit of proportionality on a graph?
Reveal answer and marking guidance
Answer: It is where the graph stops being a straight line through the origin.
Marking: Credit departure from proportional straight-line behaviour.
Exam practice ladder
Answers and marking guidance
The exact practice answers are hidden under each question so you can try first. For this lesson, marks come from using the correct physics model, choosing the right equation where needed, keeping units with values, and explaining changes with precise words such as transfer, resultant force, acceleration, evidence and uncertainty.
Common mistakes
- Using total length instead of extension.
- Forgetting to convert centimetres to metres.
- Assuming Hooke's law applies after the graph curves.
- Confusing elastic deformation with elastic potential energy.
Exam-board guidance
All supported routes assess the core physics idea, but they may group topics, practicals and paper wording differently.
AQA GCSE Physics
AQA GCSE Physics: use this lesson for hooke's law, spring constant and elastic energy, then check whether your class is taking Separate Physics or Combined Science.
OCR GCSE Physics
OCR GCSE Physics: the core physics idea is shared, but Gateway and Twenty First Century may organise questions differently.
Pearson Edexcel GCSE Physics
Pearson Edexcel GCSE Physics: practise the concept, the equation use and the practical language because questions often connect them.
Eduqas GCSE Physics
Eduqas GCSE Physics: learn the core explanation and practise applying it to unfamiliar contexts, data and practical questions.
WJEC Wales
WJEC Wales: check whether your class is using the current GCSE Physics route or a newer science route, then use this lesson for the shared physics idea.
CCEA GCSE Physics
CCEA GCSE Physics: connect the idea to your unit and remember that practical skills are assessed directly.
Extension challenge
Sketch a force-extension graph with the limit of proportionality labelled, then explain the gradient in the straight-line region.
Reveal answer
Example answer: A strong extension response names the physics model, uses accurate units and explains why the evidence supports the conclusion.
Next lesson
Next, continue with Work Done, Power and Energy Transfer.