4.7.6 Energy Conservation

Loading and Unloading a Metal Wire

• When a metal wire is loaded with a force and stretched beyond its limit of proportionality, it will undergo plastic deformation
• When the force is removed, the wire is unloaded, this causes the extension to decrease
• The unloading line is parallel to the loading line (since k does not change) however, it does not go through the origin
  • If the wire is permanently deformed, it will not be at zero extension when there is no force as it is now permanently extended

• The area between the loading and unloading lines represents the work done to permanently deform the wire

Force-extension graph of a material that has undergone plastic deformation

Loading and Unloading a Rubber Band

• The force-extension graph for a material may not always be the same when loading (adding a force) and unloading (removing a force)
• The force-extension curve for stretching and contracting a rubber band is shown below

Loading and unloading on a force-extension graph

• Since the rubber band has no extension when the load is fully removed, it has no permanent extension
  • This means that the rubber band is elastic

• The graph shows the rubber band stores a greater amount of strain energy when it is loaded (stretched) than when it is being unloaded (contracted)
• The curve for contraction is always below the curve for stretching
• The key features of the area under the graph are:
  • Area X is the work done in heating the rubber (or the increase in thermal energy)
  • Area Y is the work done by the rubber when it is returned to its original shape
  • Area X + Y represents the work done in stretching the rubber band originally

• However, due to the conservation of energy, the difference in strain energy when loading and unloading must be accounted for
• A rubber band becomes warm when it is stretched and contracted hence some energy is transferred to heat energy

• Vehicle suspension systems are made up of tires, springs and shock absorbers which provide comfortable handling of a vehicle and improve the comfort of passengers
• Roads are often very bumpy filled with potholes and speed bumps
  • A bump in the road causes the wheel of a vehicle to move up and down perpendicular to the road surface.
  • If a wheel loses contact with the road surface, it will slam back down again causing large vibrations within the car and potentially damage the vehicle
  • As well as this it would be very uncomfortable for the passengers and the driver could lose control of the vehicle

Vehicle suspension, springs and shock absorbers above the wheel help absorb any impact forces

• This energy is absorbed by shock absorbers
  • These are elastic objects designed to absorb or dampen the compression and rebound of the springs above a vehicle’s tires
  • They help keep the tires on the road at all times

• When a vehicle hits a bump in a road, the shock absorbers dampen the movement of the springs in the suspension system
  • They do this by converting kinetic energy, from the movement of the car, into thermal energy which is dissipated

• The faster the springs in the suspension system move (say, if a vehicle hits a bump at a high velocity), the more resistance the shock absorber provides