Educator

Energy: Gravitational Potential

• We can think of potential energy as energy stored for future use. This isn't perfectly rigorous, but it gives us a good understanding for now.
• The amount of gravitational potential energy is based off of the mass of the object, the gravity involved, and the height of the object:
  

  Egravity = mgh.

• We have to set the "base" height. Remember, as usual, we're the ones who have to impose a coordinate system, so it's up to us to determine what we consider the starting height.
• Because of this, the important thing isn't the "absolute" height, but instead the relative height between the start and end heights: ∆h.
• This formula relies on the fact that g is a constant near the surface of Earth (or whatever gravitational body we're dealing with). If g were to vary over the height traveled, we would need a different formula.
• 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.]
• It's up to decide when we want to take our start and end "snapshots." Carefully choosing what moments we want to compare is key to solving problems.