Energy Diagrams

The basic idea of an energy diagram is to pictorially represent approximately how the energy is divided among the relevant energy categories at each time of interest.  At the very least there will be two diagrams, one for before and the other after, though sometimes there will also be intermediate times that need to be drawn.  The energy diagram will be represented by a bar chart, with each bar representing the amount of energy in that particular energy category.  For example:
shows a fair amount of energy in gravitational potential energy, some kinetic energy, and a small amount of energy in the Internal category (usually in the form of heat produced by friction).

Steps in drawing an energy diagram (example)

  1. Identify all the times of interest for which a diagram needs to be drawn.  This will usually include all the times in which information about the situation is given and/or values you are asked to solve for.  In most problems there will be a beginning and an end diagram, with possibly times in between.  Draw an axis for each time and label what time it is.
  2. Identify all the types of energy that are involved at least one of the times.  See chart below to help identify types.  Label the horizontal axis of each chart with the types of energy.
  3. In each chart, draw a bar to represent the approximate amount of energy for each category at each time.  In particular pay attention to when there will be no energy in that category: no kinetic energy if not moving, no gravitational potential energy if at the zero reference point, no spring energy if spring is at equilibrium position, no internal energy if frictionless, etc.  Note that the sum of the heights of the diagrams should be the same for each chart.
  4. Using the diagrams, write down the sum of all the energies that are present at each time, and set them equal to those of a different time.

Types of energy that could be included

Name Description Symbol Amount
Linear Kinetic energy Energy something has because it is moving. KE 0.5mv2
Gravitational potential energy Potential energy due to gravitational force GPE or PEg mgh
Spring potential energy Potential energy due to compressed or stretched spring. SPE or PEs 0.5kx2
Internal energy Energy dissipated due to friction, deformation IE Fdcos(theta)
Muscle, chemical, electrical, etc. Energy brought into system from muscles, fuel in an engine, electricity, etc. Fdcos(theta)
Rotational kinetic energy Energy something has because it is rotating KErot or RKE 0.5Iw2
Other forms of energy not normally encountered in Physics 201:
Electrostatic, Magnetic, light, nuclear, thermal, chemical, etc.