# Elastic potential energy

Figure 1. Elastic potential energy stored by a spring.[1]

The Potential energy stored in a spring (or any similar object) is known as the elastic potential energy. It is stored by the deformation of an elastic material such as the spring in Figure 1.[2]

## Background

The energy stored in a spring depends on the distance the spring is deformed (stretched or compressed) and the spring constant, which defines the amount of force required to deform a spring by a certain length (the work done on the spring).[3] The ability to get energy out depends on the material's elasticity.

Elastic potential energy is given by the equation:[3]

$E_{elastic}= \frac{1}{2}{k}{x^2}$ where,

$E_{elastic}$: elastic potential energy (Joules, J)

$k$: elastic constant (Newtons per meter, N/m)

$x$: distance of stretching (meters, m)

The elastic properties of a spring depends on both shape and the material of the spring. Therefore, the elastic constant is different for every object. Elastic potential energy increases with the constant of the spring and with the distance stretched.[2]

## Application

A spring is used to store elastic potential energy in many mechanical devices (like the shock absorbers in cars). This energy can be used in many ways since the spring can remain in its compressed or stretched state for extended periods of time without dissipating energy.[3]

Spring potential can also be utilized in control systems or mechanical systems to reduce the impact of disturbance, such as in motor vehicles. In vehicles, the shock absorbers are springs that absorb the energy created by hitting bumps in the road, preventing the energy from disrupting the passenger compartment of the vehicle. Another use of spring potential in vehicles is in regenerative braking systems, where the stored energy is used to give the vehicle a small power boost.

## Elastic vs. plastic deformation

Changing the shape of a system takes energy. If the energy comes back out when the pressures and forces are released, that deformation is called elastic deformation (and makes elastic potential energy). Plastic deformation is the energy that is put into the system that doesn't come back out; for example, when two cars collide, much of their energy goes into changing the shape of the cars.[4]

Plasticity means that when something is stretched, it stays stretched. When an object stays stretched (or bent), that process is called plastic deformation. When the material goes back to its original form, that's elastic deformation.[5]

All springs have some plastic deformation, so some energy is always lost. Plastic deformation causes the atoms to speed up in the spring, raising the temperature of the material (similar to, but different from friction), which is why the hoods of cars are quite hot after a car accident. Elastic potential energy is the energy that comes back out, so that doesn't increase the temperature.

## Reference

1. Wilson, Tracy. (2014, Aug. 14). How Crossbows Work [Online]. Available: http://science.howstuffworks.com/crossbow2.htm
2. Landau, L.D. and Lifshitz, E. M., Theory of Elasticity, 3rd ed. Oxford, England: Butterworth Heinemann, 1986, Ch. 2.
3. R. D. Knight, "Springs," in Physics for Scientists and Engineers: A Strategic Approach, 2nd ed. San Francisco: Pearson Addison-Wesley, 2008, pp. 281-284.
4. R. D. Knight, "Inelastic collisions," in Physics for Scientists and Engineers: A Strategic Approach, 2nd ed. San Francisco: Pearson Addison-Wesley, 2008, pp. 284-287.
5. Hawkes et al, "Deformation and Elasticity," in Physics for Scientists and Engineers 1st ed. Toronto: Cengage, 2014, pp. 265-268.

## Authors and Editors

Allison Campbell, Jordan Hanania, Braden Heffernan, James Jenden, Kai, Matthew Tierney, Jason Donev