OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(b) elastic potential energy; E = 1/2 Fx; E = 1/2 kx²
Full specification wording
Mechanical properties of matter: (b) elastic potential energy; E = 1/2 Fx; E = 1/2 kx²
Elastic potential energy is the energy stored in a material when it is stretched or compressed elastically, and it is recovered when the deforming force is removed.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 2 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Elastic potential energy is the energy stored in a material when it is stretched or compressed elastically, and it is recovered when the deforming force is removed. For a material obeying Hooke's law, the stored energy equals the work done, which is the area under the force–extension graph: E = ½Fx, where F is the final force and x is the extension. Since F = kx, substituting gives E = ½kx², where k is the force constant in N m⁻¹. Both expressions apply only while the limit of proportionality is not exceeded.
For example: A spring of force constant 200 N m⁻¹ stretched by 0.10 m stores E = ½ × 200 × (0.10)² = 1.0 J.
What earns the marks
- Elastic potential energy is the energy stored when a material is elastically stretched or compressed.
- E = ½Fx applies to a straight-line force–extension graph through the origin, where F is the final force and x the extension.
- E = ½kx² follows from substituting F = kx, with k the force constant in N m⁻¹.
- The expressions apply only up to the limit of proportionality; beyond it the stored energy is not given by these equations.
Common mistakes and how to put them right
Using the full force throughout the extension.
Put it right: The average force is ½F, which is why the factor ½ appears.
Forgetting to square the extension in E = ½kx².
Put it right: Square x before multiplying.
Applying the equations beyond the limit of proportionality.
Put it right: They hold only for straight-line Hooke's law behaviour.
Exam tips
- Write down the equation, substitute values with units, then evaluate to avoid order-of-operation errors.
- Check that the extension is in metres before squaring it in E = ½kx².
- If the material has been stretched beyond the limit of proportionality, state that these equations no longer apply.
Try the lesson
The start of the Mechanical properties of matter: (b) elastic potential energy; E = 1/2 Fx; E = 1/2 kx² lesson, made from checked teaching notes for this specification point.
Listen
Elastic potential energy is the energy stored in a material when it is stretched or compressed elastically, and it is recovered when the deforming force is removed. For a material obeying Hooke's law, the stored energy equals the work done, which is the area under the force–extension graph: E = ½Fx, where F is the final force and x is the extension. Since F = kx, substituting gives E = ½kx², where k is the force constant in N m⁻¹. Both expressions apply only while the limit of proportionality is not exceeded. For example, a spring of force constant 200 N m⁻¹ stretched by 0.10 m stores E = ½ × 200 × (0.10)² = 1.0 J. A strong answer earns marks for these points. Elastic potential energy is the energy stored when a material is elastically stretched or compressed. E = ½Fx applies to a straight-line force–extension graph through the origin, where F is the final force and x the extension. E = ½kx² follows from substituting F = kx, with k the force constant in N m⁻¹. The expressions apply only up to the limit of proportionality; beyond it the stored energy is not given by these equations. A common slip: Using the full force throughout the extension. Instead, the average force is ½F, which is why the factor ½ appears. Exam tip: Write down the equation, substitute values with units, then evaluate to avoid order-of-operation errors.
See it
Put it in order
Put these steps in the order they happen.
- 1. Valid only up to the limit of proportionality
- 2. E = ½kx²
- 3. Work done = area under force–extension graph
- 4. Substitute F = kx
- 5. Material stretched or compressed elastically
- 6. Energy stored as elastic potential energy
- 7. E = ½Fx
Key words
Say what each word means before you turn the card.
Elastic potential energy
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Hooke's law
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Force constant
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Limit of proportionality
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See every definition
- Elastic potential energy
- The energy stored in a material when it is stretched or compressed elastically, recovered when the deforming force is removed.
- Hooke's law
- Behaviour in which the force–extension graph is a straight line through the origin, so that F = kx.
- Force constant
- The constant k in F = kx, measured in N m⁻¹.
- Limit of proportionality
- The point up to which the expressions for stored energy apply; beyond it the stored energy is not given by these equations.
Label the diagram
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1Box 1
2Box 2
3Box 3
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