OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Forces in action: calculate the work done in stretching
Stretching a spring transfers energy to it as elastic potential energy, and the work done equals the area under the force–extension graph.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 12 of 21
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Stretching a spring transfers energy to it as elastic potential energy, and the work done equals the area under the force–extension graph. In linear cases the graph is a straight line from the origin, so the area is a triangle and the work done is W = ½Fx, where F is the final force in newtons and x the extension in metres. A spring stretched by 8 N through 0.05 m stores W = ½ × 8 × 0.05 = 0.2 J. The half appears because the force rises from zero to F as the spring stretches, so the average force is F ÷ 2. Convert extension to metres so the answer is in joules. Do not use W = Fx with the full force, which would overestimate the energy.
What earns the marks
- States or selects W = ½Fx for the work done in stretching a linear spring.
- Uses the final force and the extension, converting the extension to metres.
- Multiplies half the force by the extension and gives the answer in joules.
- Explains that the factor of one half arises because the force increases from zero to its final value.
- Links the work done to the elastic potential energy stored in the stretched spring.
Common mistakes and how to put them right
Uses W = Fx with the full force and omits the factor of one half; use W = ½Fx.
Leaves the extension in centimetres so the energy is wrong.
Put it right: Convert to metres first.
Uses the total length rather than the extension.
Put it right: Subtract the original length.
Exam tips
- Write W = ½Fx, substitute the numbers, then state the unit as joules.
- Convert extension to metres before calculating so the energy is in joules.
- Check the answer is smaller than F × x, since the average force is only half the final force.
Try the lesson
The start of the Forces in action: calculate the work done in stretching lesson, made from checked teaching notes for this specification point.
Have a go first
A spring with a spring constant of 100 N/m is stretched by 0.2 m. Using the average force, what work is done in stretching it?
Listen
Stretching a spring transfers energy to it as elastic potential energy, and the work done equals the area under the force–extension graph. In linear cases the graph is a straight line from the origin, so the area is a triangle and the work done is W = ½Fx, where F is the final force in newtons and x the extension in metres. A spring stretched by 8 N through 0.05 m stores W = ½ × 8 × 0.05 = 0.2 J. The half appears because the force rises from zero to F as the spring stretches, so the average force is F ÷ 2. Convert extension to metres so the answer is in joules. Do not use W = Fx with the full force, which would overestimate the energy. A strong answer earns marks for these points. States or selects W = ½Fx for the work done in stretching a linear spring. Uses the final force and the extension, converting the extension to metres. Multiplies half the force by the extension and gives the answer in joules. Explains that the factor of one half arises because the force increases from zero to its final value. Exam tip: Write W = ½Fx, substitute the numbers, then state the unit as joules.
Key words
Say what each word means before you turn the card.
Work done in stretching
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Elastic potential energy
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Area under a force–extension graph
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Linear spring behaviour
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See every definition
- Work done in stretching
- Equals the area under the force–extension graph, and in linear cases is W = ½Fx, where F is the final force and x the extension.
- Elastic potential energy
- Energy transferred to a spring when it is stretched, equal to the work done in stretching it.
- Area under a force–extension graph
- Gives the work done in stretching; in linear cases the graph is a straight line from the origin, so the area is a triangle.
- Linear spring behaviour
- The graph is a straight line from the origin, so the area is a triangle and the work done is W = ½Fx.
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