Force and Extension
Revise Force and Extension for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Investigate how the extension of a spring varies with the force applied, and identify the limit of proportionality.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
This required practical investigates the relationship between the force applied to a spring and its extension.
A spring is hung from a clamp stand with a ruler fixed vertically alongside it. The unstretched length is recorded, then masses are added one at a time and the new length recorded each time. The extension is calculated by subtracting the original length from each new length.
A graph of force against extension gives a straight line through the origin while Hooke's law holds, and the gradient is the spring constant. Beyond the limit of proportionality the line curves. The work done in stretching a spring equals the area under the force-extension graph.
Revision notes
The method
Hang the spring from a clamp stand with a ruler fixed vertically alongside, and record the unstretched length.
Add masses one at a time, recording the new length each time. Weight = mass × gravitational field strength gives the force. Extension = new length − original length.
The graph
Plot force on the vertical axis against extension on the horizontal axis.
While Hooke's law holds the graph is a straight line through the origin, and its gradient equals the spring constant. Beyond the limit of proportionality the line begins to curve.
Area under the graph
The work done in stretching a spring is equal to the area under the force-extension graph.
For a straight line this is a triangle, so the area is ½ × force × extension, which is the same as the elastic potential energy stored.
Key points
- Record the unstretched length first.
- Extension = new length − original length.
- Force is found from the mass added.
- The graph is a straight line through the origin.
- The gradient gives the spring constant.
- The area under the graph is the work done.
Worked examples
Example 1
A spring of original length 5 cm stretches to 9 cm. Calculate the extension in metres. [2 marks]
Model answer
Extension = 9 − 5 = 4 cm (1 mark), which is 0.04 m (1 mark).
Example 2
Explain what the gradient of a force-extension graph represents. [2 marks]
Model answer
The gradient represents the spring constant of the spring (1 mark), because force is directly proportional to extension and the constant of proportionality is the spring constant (1 mark).
Example 3
Explain how the graph shows that the limit of proportionality has been exceeded. [2 marks]
Model answer
The line stops being straight and begins to curve (1 mark), showing that extension is no longer directly proportional to the force applied (1 mark).
Common mistakes
Plotting length instead of extension.
The extension must be calculated by subtracting the original length.
Forgetting to convert the mass to a force.
Weight = mass × g gives the force applied.
Reading the spring constant as the y-intercept.
It is the gradient of the line.
Not identifying where the line curves.
That point is the limit of proportionality and is often asked about.
Exam tips
- Record the unstretched length before adding any masses.
- Convert mass to weight before plotting force.
- Use the gradient for the spring constant.
- Identify the curve as the limit of proportionality.
Key terms
- Extension
- The increase in length from the original length.
- Gradient
- The steepness of a graph, giving the spring constant here.
- Limit of proportionality
- Where the graph stops being a straight line.
- Clamp stand
- Apparatus holding the spring vertically.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.