workEnergy transferred by a force. Work done = force Ă— distance moved in the direction of the force. is done when a spring is extensionIncrease in length, for example, as a result of being pulled. or compressionAÂ shortening in length, for example, as a result of being squeezed.. elastic potential energyEnergy stored in squashed, stretched or twisted materials. is stored in the spring. Provided inelastic deformation has not happened, the work done is equal to the elastic potential energy stored.
The elastic potential energy stored can be calculated using the equation:
elastic potential energy = 0.5 Ă— spring constant Ă— (extension)2
\(E_e = \frac{1}{2}~k~x^2\)
This is when:
elastic potential energy (Ee) is measured in joules (J)
spring constant (k) is measured in newtons per metre (N/m)
extension, referring to the increase in length (x) is measured in metres (m)
This equation also works for the reduction in length when a spring is compressed.
Example
A spring has a spring constant, k, of 3 N/m. It is stretched until it is extended by 50 cm. Calculate the elastic potential energy stored by the spring, assuming it is not stretched beyond the limit of proportionality.
First convert centimetres to metres:
\(50~cm = \frac{50}{100} = 0.5~m\)
Then calculate using the values in the question:
\(E_x = \frac{1}{2}~k~x^2\)
\(E_x = \frac{1}{2} \times 3 \times 0.5^2\)
\(E_x = 1.5 \times 0.25\)
\(E_x = 0.375~J\)
Question
A spring is compressed by 0.15 m. It has a spring constant of 80 N/m. Calculate the elastic potential energy stored by the spring.
\(E_x = \frac{1}{2}~k~x^2\)
\(E_x = \frac{1}{2} \times 80 \times 0.15^2\)
\(E_x = 40 \times 0.0225\)
\(E_x = 0.90~J\)
It is not only springs that store elastic potential energy.