4.2.3

# Energy in Materials

Test yourself

## Energies in Spring Systems

In a simple spring system under a load, the spring oscillates. The total energy of the system remains constant, but the components of this energy (kinetic, gravitational potential and elastic potential) can vary.

### Total energy

• A spring system obeys the law of conservation of energy.
• The total energy at all points in an oscillation is the same.

### Elastic potential energy

• Elastic potential energy stored in a spring is:
• $E = \frac{1}{2} F \Delta L$
• This is equal to the area under a force-extension graph.
• Using Hooke's law ($F = k\Delta L$):
• $E = \frac{1}{2} k (\Delta L)^2$

## Energy Conservation in Transport Design

Safety features of vehicles rely on specific material properties.

### Energy issues

• In an impact (such as a car crash), a great deal of energy can be transferred to the passengers.
• This could cause significant injury. Vehicles are designed to redirect this energy away from passengers.

### Crumple zones

• Crumple zones are parts of a vehicle which permanently deform.
• Crumple zones show plastic behaviour.
• The energy of impact is redirected towards plastically deforming the crumple zones. So people are less likely to be injured.