Elastic Potential Energy (OCR A Level Physics)

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 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

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:

• 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

v ∝ x

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