AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Energy stored = F∆L = area under force−extension graph Description of…
Full specification wording
Bulk properties of solids: energy stored = F∆L = area under force−extension graph Description of plastic behaviour, fracture and brittle behaviour linked to force–extension graphs.
The energy stored in a stretched material equals the area under its force–extension graph.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 4 of 8
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The energy stored in a stretched material equals the area under its force–extension graph. For a straight-line Hooke's law region, this is ½FΔL; for curved regions, the area is found by counting squares. Plastic behaviour occurs beyond the elastic limit, where the material does not return to its original length when the force is removed, leaving a permanent extension. Fracture is the point at which the material breaks, shown where the graph ends. Brittle behaviour means a material fractures with little or no plastic deformation, which is distinct from stiffness. Comparing graphs allows the elastic limit, yield point, ultimate tensile force and breaking point to be identified.
For example: A brittle glass wire snaps suddenly, whereas ductile copper shows a large plastic region.
What earns the marks
- State that energy stored equals the area under the force–extension graph; for a straight-line region this is ½FΔL.
- Calculate the energy stored in curved regions by graphically counting squares under the curve.
- Describe plastic behaviour as occurring beyond the elastic limit, resulting in permanent deformation when the force is removed.
- Identify fracture as the point on the force–extension graph at which the material breaks and the force falls to zero.
- Describe brittle behaviour as fracture occurring with little or no plastic deformation, independent of the graph's initial gradient.
Common mistakes and how to put them right
Treating the whole area under a curved loading graph as recoverable elastic strain energy when stretched beyond the elastic limit.
Put it right by recognising that the recoverable energy is the area under the unloading curve, while the hysteresis loop represents dissipated energy.
Assuming a brittle material has a low breaking stress.
Put it right by understanding that brittleness refers to little plastic deformation before fracture, not the breaking stress value.
Confusing brittleness with stiffness.
Put it right by recognising that a brittle material can have a low or high stiffness (gradient), as brittleness only relates to the lack of plastic deformation.
Exam tips
- Label the elastic limit, yield point, ultimate tensile force and fracture point on a sketch graph before answering comparison questions.
- When calculating energy stored from a curved graph, count squares under the curve and explicitly state the area scale used.
Try the lesson
The start of the Bulk properties of solids: energy stored = F∆L = area under force−extension graph Description of plastic behaviour, fracture and brittle behaviour linked to force–extension graphs. lesson, made from checked teaching notes for this specification point.
Have a go first
A force of 12 N produces an extension of 0.25 m in a spring that obeys Hooke's law. Calculate the energy stored in the spring.
Listen
The energy stored in a stretched material equals the area under its force–extension graph. For a straight-line Hooke's law region, this is ½FΔL; for curved regions, the area is found by counting squares. Plastic behaviour occurs beyond the elastic limit, where the material does not return to its original length when the force is removed, leaving a permanent extension. Fracture is the point at which the material breaks, shown where the graph ends. Brittle behaviour means a material fractures with little or no plastic deformation, which is distinct from stiffness. Comparing graphs allows the elastic limit, yield point, ultimate tensile force and breaking point to be identified. For example, a brittle glass wire snaps suddenly, whereas ductile copper shows a large plastic region. A strong answer earns marks for these points. State that energy stored equals the area under the force–extension graph; for a straight-line region this is ½FΔL. Calculate the energy stored in curved regions by graphically counting squares under the curve. Describe plastic behaviour as occurring beyond the elastic limit, resulting in permanent deformation when the force is removed. Identify fracture as the point on the force–extension graph at which the material breaks and the force falls to zero. A common slip: Treating the whole area under a curved loading graph as recoverable elastic strain energy when stretched beyond the elastic limit. Instead, recognising that the recoverable energy is the area under the unloading curve, while the hysteresis loop represents dissipated energy. Exam tip: Label the elastic limit, yield point, ultimate tensile force and fracture point on a sketch graph before answering comparison questions.
See it
Key words
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Graphical determination of stored energy
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Plastic deformation and permanent extension
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Fracture and breaking point
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Brittle versus ductile force–extension graphs
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See every definition
- Graphical determination of stored energy
- Energy stored equals the area under the force–extension graph; for a straight-line region this is ½FΔL, and for curved regions the area is found by counting squares.
- Plastic deformation and permanent extension
- Occurs beyond the elastic limit, where the material does not return to its original length when the force is removed, leaving a permanent extension.
- Fracture and breaking point
- The point at which the material breaks, shown where the graph ends and the force falls to zero.
- Brittle versus ductile force–extension graphs
- Brittle behaviour means a material fractures with little or no plastic deformation, which is distinct from stiffness, whereas ductile copper shows a large plastic region.
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