Work Done on a Mass (AQA A Level Physics): Revision Note

Work Done on a Mass

• When a mass is moved against the force of gravity, work is done

• The work done in moving a mass  is given by:

• Where:

  • = change in work done (J)

  • = mass (kg)

  • = change in gravitational potential (J kg^-1)

Change in gravitational potential energy

• Two points at different distances from a mass will have different gravitational potentials

  • This is because the gravitational potential increases with distance from a mass

• Therefore, there will be a gravitational potential difference ΔV between the two points

• Where:

  • = initial gravitational potential (J kg^–1)

  • = final gravitational potential (J kg^–1)

• The change in work done against a gravitational field is equal to the change in gravitational potential energy (GPE)

  • When V = 0, then the GPE = 0

• It is usually more useful to find the change in the GPE of a system

  • For example, a satellite lifted into space from the Earth’s surface

• The change in GPE when a mass moves towards, or away from, another mass is given by:

• Where:

  • M = mass that is producing the gravitational field (e.g. a planet) (kg)

  • m = mass that is moving in the gravitational field (e.g. a satellite) (kg)

  • r₁ = first distance of m from the centre of M (m)

  • r₂ = second distance of m from the centre of M (m)

• The change in potential ΔV is the same, without the mass of the object m:

• Work is done when an object in a planet's gravitational field moves against the gravitational field lines i.e. away from the planet

Gravitational potential energy increases as a satellite leaves the surface of the Moon

Gravitational Equipotential Surfaces

• Equipotential lines (2D) and surfaces (3D) join together points that have the same gravitational potential

• These are always:

  • Perpendicular to the gravitational field lines in both radial and uniform fields

  • Represented by dotted lines (unlike field lines, which are solid lines with arrows)

• In a radial field (e.g. a planet), the equipotential lines:

  • Are concentric circles around the planet

  • Can become further apart as they move further away from the planet 

• In a radial field equipotential lines can become further apart as they move further away from the planet because

  • potential decreases with distance away 

  • the gravitational field gets weaker with distance away

  • a greater distance needs to be moved to obtain the same change in potential, ΔV

In a radial field equipotential lines are concentric circles around the object

• In a uniform field (eg. near the Earth's surface), the equipotential lines are:

  • Horizontal straight lines

  • Parallel

  • Equally spaced

• No work is done when moving along an equipotential line or surface, only between equipotential lines or surfaces

  • This means that an object travelling along an equipotential doesn't lose or gain energy and ΔV =  0

Gravitational equipotential lines in a uniform gravitational field are equally spaced