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2.1.3Energy

Gravitational Potential Energy

5 min read 5 parts Lesson 4 of 16 1 quiz

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Section 1 of 5The Gravitational Potential Store

2.1.3 Gravitational Potential Energy

An object gains energy in this store when it is raised against its weight.

Lifting
  • Raising an object against its weight does work on it, transferring energy into its gravitational potential store.
Falling
  • As an object falls, its gravitational potential store empties and the energy is transferred to its kinetic store.
Vertical height
  • Only the vertical change in height counts, so the energy depends on how far the object rises, not the length of a slope.
Mass versus weight
  • Mass is the amount of matter and stays the same everywhere, whereas weight depends on the local gravitational field strength.

Section 2 of 5Gravitational Field Strength

Gravitational Field Strength
Earth
  • Approximately 9.8 N/kg at the surface, a value usually supplied in examination questions.
Moon
  • Weaker than on Earth, roughly one sixth as strong, so the same mass gains less energy when lifted through the same height.
Gas giants
  • Stronger than on Earth at their surfaces, so lifting a mass through a given height transfers more energy.
Mass
  • The mass of an object does not change with location, even though its weight and the energy gained do.

Section 3 of 5Using the Equation

1
List the mass in kilograms, the gravitational field strength in N/kg and the vertical height in metres.
2
Write the equation ΔEp = m × g × Δh and substitute the known values into it.
3
Multiply the numbers together and give the answer in joules, to two or three significant figures.

Section 4 of 5Worked Example

Question

  • A 12 kg box is lifted vertically through 4.0 m.
  • Take g = 9.8 N/kg.
  • Calculate the increase in its gravitational potential energy.

  1. Known quantitiesm = 12 kg, g = 9.8 N/kg, Δh = 4.0 m
  2. EquationΔEp = m × g × Δh
    What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)
  3. SubstituteΔEp = 12 × 9.8 × 4.0 = 470.4 J

Answer ΔEp ≈ 470 J (2 significant figures).

Section 5 of 5Exam Checklist & Tips

2.1.3 – Key Points for the Exam

  • Gravitational potential store The store of energy an object holds because of its height in a gravitational field.
  • Gravitational field strength The force per unit mass due to gravity at a point, measured in N/kg.
  • Vertical height The straight-line height an object is raised, measured in metres.
  • Weight The gravitational force acting on an object, measured in newtons.
  • Mass The amount of matter in an object, measured in kilograms.

Common Mistakes

  • Using the length of a slope instead of the vertical height in ΔEp = m × g × Δh.
  • Confusing mass in kilograms with weight in newtons.
  • Giving the gravitational potential energy in newtons rather than joules.
  • Stating that a change in gravitational field strength changes the mass of the object.
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