OCR A Level Physics

Revision Notes

3.7.4 Elastic Potential Energy

Test Yourself

Area under a Force-Extension Graph

  • Work has to be done to stretch a material
  • Before a material reaches its elastic limit (whilst it obeys Hooke's Law), all the work done is stored as elastic strain energy
  • The work done, or the elastic strain energy is the area under the force-extension graph

Work done under graphs, downloadable AS & A Level Physics revision notes

Work done is the area under the force-extension graph

  • This is true for whether the material obeys Hooke’s law or not
    • For the region where the material obeys Hooke’s law, the work done is the area of a right-angled triangle under the graph
    • For the region where the material doesn’t obey Hooke’s law, the area is the full region under the graph. To calculate this area, split the graph into separate segments and add up the individual areas of each

Worked example

The graph shows the behaviour of a sample of a metal when it is stretched until it starts to undergo plastic deformation.WE - Work done area under graph question image, downloadable AS & A Level Physics revision notesWhat is the total work done in stretching the sample from zero to 13.5 mm extension?

Simplify the calculation by treating the curve XY as a straight line.

WE - Work done area under graph answer image (1), downloadable AS & A Level Physics revision notesWE - Work done area under graph answer image (2), downloadable AS & A Level Physics revision notes

Worked example

A spring is extended with varying forces; the graph below shows the results.WE - EPE area under graph question image, downloadable AS & A Level Physics revision notesWhat is the energy stored in the spring when the extension is 40 mm?

WE - EPE area under graph answer image, downloadable AS & A Level Physics revision notes

Exam Tip

Remember to always double-check the units on the force and extension axes on the graph before using values from it for calculations. The force can sometimes be in kN and the extension in mm!

Elastic Potential Energy

  • Elastic potential energy is defined as

The energy stored within a material (e.g. in a spring) when it is stretched or compressed

  • It can be found from the area under the force-extension graph for a material deformed within its limit of proportionality
  • A material within its limit of proportionality obeys Hooke’s law
  • Therefore, for a material obeying Hooke’s Law, elastic potential energy can be calculated using:

Hooke's law EPE, downloadable AS & A Level Physics revision notes
  • Where:
    • k = force constant of the spring (N m-1)
    • x = extension (m)

  • It is very dangerous if a wire under stress suddenly breaks
  • This is because the elastic potential energy of the strained wire is converted into kinetic energy

EPE = KE

½ kx2 = ½ mv2

vx

  • This equation shows that the greater the extension of a wire, x, the greater the speed, v, it will have on breaking

Worked example

A car’s shock absorbers make a ride more comfortable by using a spring

that absorbs energy when the car goes over a bump. One of these

springs, with a force constant of 50 kN m-1 is fixed next to a wheel and compressed a distance of 10 cm.Calculate the energy stored by the compressed spring.

Step 1: List the known values

    • Force constant, k = 50 kN m-1 = 50 × 103 N m-1
    • Compression, x = 10 cm = 10 × 10-2 m

Step 2: Write the relevant equation

EPE = ½ kx2

Step 3: Substitute in the values

EPE = ½ × (50 × 103) × (10 × 10-2)2 = 250 J

 

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