# Physics - Elastic Potential Energy

> Source: https://ollybritton.com/notes/a-level/physics/topics/elastic-potential-energy/ · Updated: 2024-08-25 · Tags: physics, school, year-1

See also:

- [Physics - Hooke's Law](https://ollybritton.com/notes/a-level/physics/topics/hookes-law/)
- [Physics - Energy](https://ollybritton.com/notes/a-level/physics/topics/energy/)
- [Physics - Work Done](https://ollybritton.com/notes/a-level/physics/topics/work-done/)

##### What is the area under a force-extension graph??
Work done.

##### The energy put into a spring by stretching it is called??
Elastic potential energy.

##### Stretching a spring over a distance is doing what in relation to work done??
Applying a force over a distance.

##### ![PHOTO FORCE EXTENSION AREA](paste-3fdc9526df15b229f7e1ae1ec64483b8b3402d86.jpg) What does the area of the triangle represent??
Work done.

##### ![PHOTO FORCE EXTENSION AREA](paste-3fdc9526df15b229f7e1ae1ec64483b8b3402d86.jpg) What is the formula for the area of the triangle??
$$
\frac{1}{2}Fx
$$

##### ![PHOTO FORCE EXTENSION AREA](paste-3fdc9526df15b229f7e1ae1ec64483b8b3402d86.jpg) The formula for the area of the triangle is $\frac{1}{2}Fx$. How could you also write $F$??
$$
F = kx
$$

##### ![PHOTO FORCE EXTENSION AREA](paste-3fdc9526df15b229f7e1ae1ec64483b8b3402d86.jpg) Substitute $F = kx$ into $\frac{1}{2}Fx$??
$$
\frac{1}{2}kx^2
$$

##### What is the formula for elastic potential energy??
$$
E = \frac{1}{2}kx^2
$$

##### Elastic potential energy is directly proportional to...??
$$
E \propto x^2
$$

##### If you double extension, what happens to the elastic potential energy??
It quadruples.

##### How could you calculate the velocity of a compressed spring being released??
Equate kinetic energy to elastic potential energy.

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