Work, Energy and Power

• The Principle of conservation of energy states that energy cannot be created or destroyed, it can only be transferred from one form to another
• Energy stores


  Keep or store energy within one part of a system
• Types of energy stores

  • Kinetic energy
  • Gravitational potential energy
  • Magnetic energy
  • Chemical energy
  • Thermal energy
  • Nuclear energy
• Energy transfers


  Give or transfer energy to different parts of a system
• Types of energy transfers

  • Electrical
  • Mechanical
  • Heating
  • Waves
• Energy dissipation


  Energy not transferred to useful energy stores is wasted because it is lost to the surroundings
• When energy is transferred from one form to another, not all the energy will end up in the desired form (or place)
• Any energy not transferred to useful energy stores is wasted because it is lost to the surroundings
• Wasted energy is commonly in the form of thermal (heat), light, or sound energy
• What counts as wasted energy depends on the system
• In mechanical systems when energy is transferred between stores it is equivalent to the work done
• When a vertical spring is extended and contracted, its energy is converted into other forms
• Although the total energy of the spring will remain constant, it will have changing amounts of elastic potential energy, kinetic energy, and gravitational potential energy
• For a horizontal mass on a spring system, there is no gravitational potential energy to consider. The spring only converts between kinetic and elastic potential energy
• Sankey diagrams


  Used to represent energy transfers
• The width of each arrow in a Sankey diagram is proportional to the amount of energy going to each store
• Total energy in = Useful energy out + Wasted energy
• Work is defined as the transfer of energy when an external force causes an object to move over a certain distance
• The work done by the resultant force on a system is equal to the change in the energy of the system
• Sankey diagram


  A diagram that shows the flow of energy or materials through a process
• Planning a Sankey diagram

  1. Decide how wide the input arrow will be

  2. Decide how wide the 'useful energy out' arrow will be

  3. Decide how wide the 'wasted energy' arrow will be
• Drawing a Sankey diagram

  1. Draw the left hand side of the arrow, along with the line going across the top

  2. Add the 'useful energy out' arrow, making sure it is the correct width

  3. Carefully mark the start and end of the 'wasted energy' arrow - make sure the marks are the correct distance apart

  4. Join the markings to finish the 'wasted energy' arrow
• Work


  The transfer of energy when an external force causes an object to move over a certain distance
• Work done


  Equal to the change in the energy of the system
• Work done


  • If a constant force is applied in the line of an object's displacement (i.e. parallel to it), the work done can be calculated using the equation W = Fs
  • If the force is at an angle θ to the object's displacement, the work done is calculated by W = Fscosθ
• When plotting a graph of average force applied against displacement, the area under the graph is equal to the work done
• Kinetic energy


  The energy an object has due to its translational motion (i.e. because it's moving)
• Gravitational potential energy


  The energy stored in a mass due to its position in a gravitational field
• The potential energy on the Earth's surface at ground level is taken to be equal to 0
• Elastic potential energy


  The energy stored within a material (e.g. in a spring) when it is stretched or compressed
• Mechanical energy


  The sum of kinetic energy, gravitational potential energy and elastic potential energy
• The change in the total mechanical energy of a system should be interpreted in terms of the work done on the system by any non-conservative force
• Mechanical energy = Ek + ∆Ep + EH
• System with mechanical energy

  • Spring and mass system
• Change in total mechanical energy of a system


  Interpreted in terms of the work done on the system by any non-conservative force
• Energy conversion in a vertical spring

  1. Elastic potential energy

  2. Kinetic energy

  3. Gravitational potential energy
• Energy conversion in a vertical mass on a spring

  1. Elastic potential energy

  2. Kinetic energy

  3. Gravitational potential energy
• In the absence of frictional, resistive forces, the total mechanical energy of a system is conserved
• Scenarios involving transfer of kinetic energy and gravitational potential energy


  • Swinging pendulum
  • Objects in freefall
  • Sports involving falling (e.g. skiing, skydiving)
• Loss in gravitational potential energy


  Gain in kinetic energy