• Gravitational potential energy (GPE) is the energy stored in an object that is held at a height above the Earth’s surface
• The amount of gravitational potential energy an object has depends on its height and mass
• The heavier the object, and the higher it is above the ground, the more gravitational potential energy it holds
  • GPE is equal to:

• Elastic potential energy (EPE) is the energy stored in objects when they are stretched or compressed
• The more an object can stretch, the more elastic potential energy it has
  • EPE is equal to:

• The key distinction between the two:
  • Gravitational potential energy is associated with the interaction between bodies due to their masses
  • Elastic potential energy is possessed by an object due to its state of deformation

• In a uniform field, a body experiences the same force (F) at all points
• If this force moves the body along a distance Δx in its direction, then the work done (W) by this force is
  • W = FΔx
• However, by conservation of energy, this work must be compensated by a decrease in potential energy equal to −ΔU, so:
  • W = FΔx = −ΔU
• Therefore, the force acting on the point mass/charge placed at that particular point in the force field is equal to:

Worked example

• At the surface (to the right), GPE = 0
• As the object moves to the left, GPE increases
• So, GPE increases from X to Y
  • GPE = mgh
  • Weight = mg = 0.200 N
• At point X, the mass already has 1.00 J of GPE
• Therefore, GPE at Y = 1.00 + (0.2 × 0.3) = 1.06 J

• Gravitational potential energy is energy stored in a mass due to its position in a gravitational field
• When a heavy object is lifted, work is done since the object is provided with an upward force against the downward force of gravity
  • Therefore energy is transferred to the object
• This equation can therefore be derived from the work done

Derivation of GPE = mgh

• Gravitational potential energy (GPE) is energy stored in a mass due to its position in a gravitational field
  • If a mass is lifted up, it will gain GPE (converted from other forms of energy)
  • If a mass falls, it will lose GPE (and be converted to other forms of energy)
• The equation for gravitational potential energy for energy changes in a uniform gravitational field is:

Equation for GPE

GPE: The energy an object has when lifted up

• The potential energy on the Earth’s surface at ground level is taken to be equal to 0
• This equation is only relevant for energy changes in a uniform gravitational field (such as near the Earth’s surface)

GPE v Height graphs

• The two graphs below show how GPE changes with height for a ball being thrown up in the air and when falling down

Graphs showing the linear relationship between GPE and height

• Since the graphs are straight lines, GPE and height are said to have a linear relationship
• These graphs would be identical for GPE against time instead of height

Worked example