Conservation of Mechanical Energy (SL IB Physics)

• Mechanical energy is the sum of kinetic energy, gravitational potential energy and elastic potential energy

Mechanical energy = 

• An example of a system that has mechanical energy is a spring and mass system
• 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.

• 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 (E_H or EPE)
  • Kinetic energy (E_k or KPE)
  • Gravitational potential energy (E_p or GPE)

• When a vertical mass is hanging on a spring and it moves up and down, its energy will convert between the three in various amounts

• At position A:
  • The spring has some EPE since it is slightly compressed
  • Its KE is 0 since it is stationary
  • Its GPE is at a maximum because the mass is at its highest point

• At position B:
  • The spring has some EPE since it is slightly stretched
  • Its KE is at a maximum as it passes through the equilibrium position at its maximum speed
  • It has some GPE since the mass is still above the ground

• At position C:
  • The spring has its maximum EPE because it is at its maximum extension
  • Its KE is 0 since it is stationary
  • Its GPE is at a minimum because it is at its lowest point above the Earth's surface

• 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

• In the absence of frictional, resistive forces, the total mechanical energy of a system is conserved
  • This means the total kinetic, gravitational potential and elastic potential energy is the same throughout the motion of the system
• This is essential the conservation of energy
• There are many scenarios that involve the transfer of kinetic energy into gravitational potential, or vice versa
• Some examples are:
  • A swinging pendulum
  • Objects in freefall
  • Sports that involve falling, such as skiing and skydiving

• Using the principle of conservation of energy, and taking any drag forces as negligible:

Loss in gravitational potential energy = Gain in kinetic energy

• Another example is if a ball lands on a spring from a height
• In this case:

Loss in gravitational potential energy = Gain in elastic potential energy

• The change in energy is the work done on the system. The types of changes depend on the system