Elastic potential energy
Materials - OCR A-Level Physics
Key Definition
Elastic potential energy
The energy stored in a spring or material when it is stretched or compressed within its elastic limit.
The energy stored in a spring or material when it is stretched or compressed within its elastic limit.
$$E = \frac{1}{2}kx^2$$
$$\begin{aligned}
E &= \frac{1}{2}Fx \\
&= \frac{1}{2}kx^{2}
\end{aligned}$$
- E = $\frac{1}{2}$$kx^{2}$ is the area under the linear region of a force-extension graph (a triangle)
- E = $\frac{1}{2}$Fx only applies when the force-extension relationship is linear (within the Hooke's lawThe extension of a spring is directly proportional to the applied force, provided the limit of proportionality is not exceeded. region)
- For a non-linear graph, the energyThe capacity to do work. Measured in joules (J). stored is the total area under the curve (use counting squares or trapezium rule)
- When a spring is released within the elastic limit, all stored elastic potential energy converts back to kinetic energy of the mass and the spring.
Worked Example [2 marks]
A spring with spring constantThe force per unit extension of a spring. A measure of the stiffness of the spring. Measured in N m⁻¹. 40 $N m^{-1}$ is stretched by 0.15 m. Calculate the elastic potential energyThe energy stored in a stretched or compressed spring (or other elastic object). stored.
Show Solution
1
$E = \frac{1}{2}kx^{2} = \frac{1}{2} \times 40 \times (0.15)^{2}$
[1]2
$E = \frac{1}{2} \times 40 \times 0.0225 = 0.45 \text{ J}$
[1]Answer
0.45 J
Examiner Tips and Tricks
- If the question gives F and x, use $E = 1/2 Fx$.
- If it gives k and x, use $E = 1/2 kx^2$.
- If it gives F and k, find x first from $F = kx$, then use either formula.