# PHY C9: Strain Energy

Today we’ll be covering:

• Strain Energy

Let’s go!

What is Work Done on a deformed object?
The work done by an external force (load) to change an object’s shape.
This is represented by the area underneath a force-extension graph.

In the graph above,

1. A load is first applied to the object, which causes extension.
2. After reaching the elastic limit, the object starts to behave plastically, & can no longer return to its initial shape.
3. When the load is removed, the object returns to a length that is LONGER than its initial length.

In terms of energy,

1. Work is done by an external force, causing the object to extend.
2. It stores most of this energy as elastic potential energy.
3. When the load is removed, the object recovers the stored potential energy to kinetic energy.
4. Some energy is lost as heat.

In terms of area,

• Purple + Yellow Area = Total work done by an external force ONTO the body
• Purple Area = Work done BY body ONTO external force (stored as potential energy & recovered as kinetic energy)
• Yellow Area = Energy loss (via heat)(NET work done)

When the graph is linear (deformation is fully elastic), work done or strain energy can be calculated as the area of the triangle:Strain Energy = ½Fe
Since F = ke,
Strain Energy = ½ke2

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