Educator

Energy: Elastic Potential

• If you deform an elastic object (such as a spring or rubber band), it will resist the deformation, attempting to return to its original shape.
• The amount of deformation (→x) is measured compared to its original shape. An object with no deformation has →x=0. A 0.1m spring stretched to 0.12m has the same deformation as a 1.0m spring stretched to 1.02m: →x=0.02m.
• Different objects will resist deformation at different rates. We show this with the spring constant: k (units in [N/m]).
• An elastic object resists deformation with a force of
  

  → F   spring  = −k → x   .

  The negative denotes that the force always points opposite to the deformation (→x).
• Deforming an elastic object is a way of storing energy. The amount of potential energy in a spring is
  

  Espring = 1 2 kx2.

  [When working with energy, displacement is no longer measured as a vector. Now it is simply x, the length of the displacement. This is because energy is stored whether we stretch or compress. The direction of deformation doesn't matter: just the magnitude of deformation.]
• By the conservation of energy, we can look at the entire energy of the system at the start and end:
  

  Esys,  start + W = Esys,  end.

  [Remember, positive work puts energy into the system, while negative work takes it out.]