Physics

1.6 - Elastic Potential Energy

6 min

Elastic potential energy

Finding the spring constant

Calculating the energy stored

Force-extension graphs

note 1 of 3

Stretching or squashing stores elastic potential energy

Stretching, squashing, or bending an object transfers energy to its elastic potential energy store.
An object deforms elastically when it returns to its original shape once the forces are removed.
Doing work to deform an elastic object transfers energy to its elastic potential energy store. When the spring pushes or pulls back, that energy transfers back to the object's kinetic energy store.

note 2 of 3

Formula for elastic potential energy

$E_{e} = \frac{1}{2} k e^{2}$

Where:

$E_{e}$ = Energy in the elastic potential energy store, in joules (J)
$k$ = Spring constant, in newtons per metre (N/m)
$e$ = Extension (or compression), in metres (m)

This applies as long as the spring hasn't been stretched past its limit of proportionality.

For an elastic deformation, the work done in stretching the spring equals the energy transferred to its elastic potential energy store.

note 3 of 3

Worked example - Energy stored in a stretched spring

A spring has a spring constant of 25 N/m. It is stretched elastically from a length of 0.30 m to 0.38 m. Calculate the energy transferred to its elastic potential energy store.

Step 1 - Find the extension

$\begin{matrix} e & = new length - original length \\ = 0.38 - 0.30 \\ = 0.08 m \end{matrix}$

Step 2 - Substitution and calculation

$E_{e} = \frac{1}{2} k e^{2} = \frac{1}{2} \times 25 \times {0.08}^{2} = 0.08 J$

key terms

TermDefinition

Elastic deformationA change in shape where the object returns to its original shape and length once the forces are removed.

Limit of proportionalityThe point beyond which the extension of an object is no longer directly proportional to the force applied to it.

end of notes

Key points to remember

Stretching or squashing stores elastic potential energy

Stretching, squashing, or bending an object transfers energy to its elastic potential energy store.

An object deforms elastically when it returns to its original shape once the forces are removed.

Doing work to deform an elastic object transfers energy to its elastic potential energy store. When the spring pushes or pulls back, that energy transfers back to the object's kinetic energy store.

Formula for elastic potential energy

$E_{e} = \frac{1}{2} k e^{2}$

Where:

E_{e}

= Energy in the elastic potential energy store, in joules (J)

k

= Spring constant, in newtons per metre (N/m)

e

= Extension (or compression), in metres (m)

This applies as long as the spring hasn't been stretched past its limit of proportionality.

For an elastic deformation, the work done in stretching the spring equals the energy transferred to its elastic potential energy store.

Worked example - Energy stored in a stretched spring

A spring has a spring constant of 25 N/m. It is stretched elastically from a length of 0.30 m to 0.38 m. Calculate the energy transferred to its elastic potential energy store.

Step 1 - Find the extension

$\begin{matrix} e & = new length - original length \\ = 0.38 - 0.30 \\ = 0.08 m \end{matrix}$

Step 2 - Substitution and calculation

$E_{e} = \frac{1}{2} k e^{2} = \frac{1}{2} \times 25 \times {0.08}^{2} = 0.08 J$