10.2.1 Potential & Potential Energy

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 m is given by:

• Where:
• ∆W = change in work done (J)
• m = mass (kg)
• ∆V = change in gravitational potential (J kg^-1)

• This change in work done is equal to the change in gravitational potential energy (G.P.E)

• When V = 0, then the G.P.E = 0

• The change in G.P.E, or work done, for an object of mass m at a distance r₁ from the centre of a larger mass M, to a distance of r₂ further away can be written as:

• • Where:
    • M = mass that is producing the gravitational field (eg. a planet) (kg)
    • m = mass that is moving in the gravitational field (eg. 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)

• 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

Step 1: Write down the work done (or change in G.P.E) equation

Step 2: Determine values for r₁ and r₂

r₁ is the radius of Mars = 3400 km = 3400 × 10³ m

r₂ is the radius + altitude = 3400 + 700 = 4100 km = 4100 × 10³ m

Step 3: Substitute in values

Work Done on a Charge

• When a mass with charge moves through an electric field, work is done
• The work done in moving a charge q is given by:

• Where:
• ∆W = change in work done (J)
• q = charge (C)
• ∆V = change in electric potential (J C^-1)

• This change in work done is equal to the change in electric potential energy (E.P.E)
• When V = 0, then the E.P.E = 0

• The change in E.P.E, or work done, for a point charge q at a distance r₁ from the centre of a larger charge Q, to a distance of r₂ further away can be written as:

• • Where:
    • Q = charge that is producing the electric field (C)
    • q = charge that is moving in the electric field (C)
    • r₁ = first distance of q from the centre of Q (m)
    • r₂ = second distance of q from the centre of Q (m)

Work is done when moving a point charge away from another charge

• Work is done when a positive charge in an electric field moves against the electric field lines or when a negative charge moves with the electric field lines

Step 1: Write down the known quantities

• • p.d. at R, V₁ = 675 V
  • p.d. at S, V₂ = 850 V
  • Charge, q = +3.0 nC = +3.0 × 10^-9 C

Step 2: Write down the work done equation

W = q × ΔV

Step 3: Substitute in the values into the equation

W = (3.0 × 10^-9) × (850 - 675) = 5.3 × 10^-7 J