Elastic Potential Energy

When you stretch or compress a spring (or any elastic object), you're doing work - and therefore, transferring energy. But where does that energy go? It doesn't just disappear. The energy gets stored in the spring as elastic potential energy.

When you pull back a catapult or draw back a bow and arrow, you can feel that you're doing work. All that work you're doing gets stored in the elastic material. When you let go, that stored energy is released and converts into kinetic energy (movement) - that's what fires the stone or arrow!

Elastic potential energy is the energy stored in an elastic object when it's stretched or compressed. It's a type of potential energy - "potential" because it has the potential to be released and do something useful.

Formula:

This is one of the equations given on your equation sheet, so you don't need to memorize it - but you do need to know how to use it well.

Conservation of Energy

The Law of Conservation of energy states that energy cannot be created or destroyed, only transferred from one store to another. The energy you put in by doing work must go somewhere, and in this case it's stored as elastic potential energy.

Provided the spring (or elastic object) is not inelastically deformed (see the previous Hooke’s Law page for a reminder on elastic and inelastic deformation), the work done on the spring equals the elastic potential energy stored in the spring.

Work done stretching the spring = Elastic potential energy stored:

Linear vs Non-linear Relationships

Notice that the extension is squared in this equation. This is really important, meaning Elastic potential energy is directly proportional to extension squared (), not extension. If you double the extension, you don't double the energy stored - you quadruple it (because ).

For example:

• Extension of stores a certain amount of energy

• Extension of stores as much energy (not )

• Extension of stores as much energy (not )

This non-linear relationship between elastic potential energy and extension happens because as you stretch the spring further, you're not just moving it further - you're also working against an increasing force. This is because of Hooke's Law: . As increases, increases too.

Let's think about what happens in different scenarios involving elastic potential energy:

Scenario 1: A Catapult

• You pull back the elastic (work done, energy transferred from your muscles)

• Elastic potential energy is stored in the stretched elastic

• You release it

• Elastic potential energy converts to kinetic energy of the projectile

• Projectile flies through the air

Scenario 2: A Bouncing Ball

• Ball falling has kinetic energy

• Ball hits ground and compresses

• Kinetic energy converts to elastic potential energy (and some heat)

• Ball rebounds, elastic potential energy converts back to kinetic energy

• Ball rises again (kinetic energy converts to gravitational potential energy)

Scenario 3: A Trampoline

• Person at top of jump has gravitational potential energy

• As they fall, gravitational potential energy converts to kinetic energy

• When they land, they compress the trampoline springs

• Kinetic energy converts to elastic potential energy (stored in springs)

• Springs rebound, elastic potential energy converts back to kinetic energy

• Person rises back up, kinetic energy converts to gravitational potential energy

In all these scenarios, energy is being transferred between different stores. The elastic potential energy equation lets us calculate how much energy is in the elastic potential energy store at any moment. In reality, not all the energy makes it through - some is dissipated as heat (due to air resistance and friction) and as sound.

Efficiency & Dissipation

Whenever you have energy transfers involving elastic potential energy in real situations, you need to remember that:

• Energy is never efficiently transferred

• Some energy is dissipated to the surroundings (usually as heat)

• This means actual outcomes are always less than theoretical calculations predict

For example:

• A bouncing ball doesn't bounce back to its original height

• A bungee jumper doesn't reach the full calculated height

• A catapult stone travels less far than perfect energy conservation would suggest