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Theme D — Fields

D.1.6 Gravitational Potential Energy Equation — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 8 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

D.1.6 Gravitational Potential Energy Equation — IB PHYSICS HL notes: Use W = mΔV and Ep = −GMm/r to find the work done moving a mass in a gravitational field.Cause — moving a mass against gravity needs work because gravity is attractiveEquation — W = mΔVgSymbols — W in J, m in kg…

  • Near the Earth
  • Definition
  • Potential difference
  • Energy change
  • Potential change
  • Moving away

Part 1 of 6Work done on a mass

Cause
  • Cause moving a mass against gravity needs work because gravity is attractive
Equation
  • W = mΔVg
Symbols
  • W in J, m in kg, ΔVg in J kg−1
Near the Earth
  • W = mgΔh gives ΔV = gΔh

Part 2 of 6Potential energy of two point masses

Equation
  • Ep = −Gm1m2/r
m1
  • m1 the larger mass producing the field
m2
  • m2 the mass moving in the field
r
r the distance between the centres
Definition
  • Definition the work done to assemble the system from infinite separation

Part 3 of 6Change in potential energy

Potential difference
  • ΔV = Vf − Vi
Energy change
  • ΔEp = −Gm1m2(1/r2 − 1/r1) = Gm1m2(1/r1 − 1/r2)
Potential change
  • ΔVg = Gm1(1/r1 − 1/r2)
  • It does not contain the mass of the moving object
Moving away
  • Moving away work is done against the field lines and Ep rises
Change equals work
  • Change equals work the change in potential energy is the work done

Part 4 of 6Area under the force–distance graph

Curve
  • F ∝ 1/r2
Work
  • Work the area between two points is the energy transferred
Satellite
  • Satellite moving a satellite outward means the area is the work done on it

Part 5 of 6Comparison with mgh

mgh
  • mgh only for a uniform field close to the surface
GMm/r
  • GMm/r used when g changes with distance
Inverse square
  • Inverse square g falls with distance so the new equation does not contain g
Do not confuse
  • Do not confuse the two equations look similar but refer to different situations

Part 6 of 6More from the specification

More from the specification
Gravitational Potential Energy Formulation
  • The gravitational potential energy between a spherical planet of mass M and an object of mass m separated by distance r is given by Ep = -GMm/r, with zero reference at infinity.
    • (radius R of the planet plus altitude)
Orbital Motion and Circular Speed
  • In a circular orbit around a planet, the gravitational force provides the necessary centripetal force (GMm/r² = mv²/r), establishing an orbital speed v = √(GM/r) and orbital period T = 2π√(r³/GM).
Escape Speed and Gravitational Field Strength
  • Escape speed is the minimum launch speed required for an object to break free from the gravitational field strength of a planet without additional propulsion, expressed as vesc = √(2GM/R).
Gravitational Potential Energy Formulation
  • The gravitational potential energy between a spherical planet of mass M and an object of mass m separated by distance r is given by Ep = -GMm/r, with zero reference at infinity.
    • (radius R of the planet plus altitude)
Orbital Motion and Circular Speed
  • In a circular orbit around a planet, the gravitational force provides the necessary centripetal force (GMm/r² = mv²/r), establishing an orbital speed v = √(GM/r) and orbital period T = 2π√(r³/GM).
Escape Speed and Gravitational Field Strength
  • Escape speed is the minimum launch speed required for an object to break free from the gravitational field strength of a planet without additional propulsion, expressed as vesc = √(2GM/R).
Kinetic energy
  • K = ½mv2, energy of motion.
Escape speed
  • Minimum launch speed to reach infinity, √(2GM/R).
Potential gradient
  • The rate of change of potential with distance, equal to −E
Centripetal force
  • Net force toward the centre, mv2/r.
Escape velocity
  • Minimum speed to escape a planet's gravity without further propulsion; about 11.2 km/s for Earth.
Planet
  • A large body that orbits the Sun and whose gravity clears its orbit.
Radius
  • Distance from the centre to the circular path.
Period
  • Time for one revolution.
Newton
  • Unit of force, kg m s-2.
Constant
  • Not changing.
Density
  • Mass per unit volume.
Equipotential
  • A surface of constant potential
Field strength
  • G = Fg/m.

Key terms

TermMeaning
Work done in a fieldW = mΔVg.
Gravitational potential energyEp = −Gm1m2/r for two point masses.
Change in potential energyΔEp = Gm1m2(1/r1 − 1/r2).
Potential differenceThe change in gravitational potential between two points, ΔV = Vf − Vi.

Avoid these mistakes

1
Using E = mgh for a spacecraft far from the surface.
2
Putting the radius of the planet only, without adding altitude, for r.
3
Mixing up the sign of ΔEp — it is positive moving away from the body.
4
Using the mass of the moving object when finding potential difference ΔV.
5
Treating ΔVg as having units J instead of J kg−1.

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