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Theme D — Fields

D.1.5 Gravitational Potential Energy in a Non-Uniform Field — IB Physics HL Revision Notes & Topical Questions

5 min read 7 parts Lesson 7 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.1.5 Gravitational Potential Energy in a Non-Uniform Field — IB PHYSICS HL notes: Define gravitational potential energy in a radial field and relate it to the area under a force–distance graph.Of a system — the work done to assemble the system from infinite separation of its com…

  • Of a point mass
  • What the symbols mean
  • Far from the surface
  • Newton's law
  • Moving away
  • Between two points

Part 1 of 5Gravitational potential energy in a radial field

Gravitational potential energy in a radial field
Of a system
  • Of a system the work done to assemble the system from infinite separation of its components
Of a point mass
  • Of a point mass the work done in bringing a mass from infinity to the point
Radial field
  • Radial field the energy depends on the position in the field
Sign
  • Sign it is zero at infinity and negative in the field

Part 2 of 5Near the Earth's surface

Equation
  • Ep = mgh, with zero taken at the surface
    What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)
Uniform field
  • Uniform field it applies only because the field is approximately uniform close to the surface
Far from the surface
  • Far from the surface the field is radial because the Earth is a sphere, so mgh fails
Use
  • Use mgh is rarely needed in this topic

Part 3 of 5Force–distance graph

Newton's law
  • F = GMm/r2 so F ∝ 1/r2 and the graph is a curve
Area
  • Area force × distance is work, so the area under the graph is the energy transferred
Moving away
  • Moving away gravity is attractive so work is done on the mass and its potential energy rises
Between two points
  • Between two points the area gives the change in gravitational potential energy

Part 4 of 5Link to potential

Relation
  • Relation the potential energy of a mass m is Ep = mVg
Difference from g
  • Difference from g the energy includes the mass m of the object, while Vg does not
Data booklet
  • Data booklet this equation is not given, but its meaning must be understood

Part 5 of 5More from the specification

More from the specification
Non-uniform potential energy
  • Non-uniform potential energy integrating gravitational attraction across radial radial distances provides an exact mathematical means to calculate binding energy.
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.
Satellite
  • A body that orbits a larger one; the Moon is the Earth's natural satellite.
Period
  • Time for one revolution.
Constant
  • Not changing.
Density
  • Mass per unit volume.
Equipotential
  • A surface of constant potential
Field strength
  • G = Fg/m.
Field lines
  • Lines showing the direction and strength of a magnetic field.
Orbital period
  • Time for one orbit.
Orbital radius
  • Orbital radius r is measured from the planet's centre, so add the planet's radius to the height above its surface.

Key terms

TermMeaning
Gravitational potential energyThe work done in bringing a mass from infinity to a point in a gravitational field.
Radial fieldA non-uniform field whose lines meet at the centre of a sphere.
Uniform fieldA field with the same strength at all points, shown by parallel lines.
Area under F–r graphThe work done, equal to the change in potential energy.

Avoid these mistakes

1
Using Ep = mgh for large heights — the field is not uniform there.
2
Taking the area under a force–distance graph as force.
3
Forgetting that potential energy is negative in a radial field.
4
Leaving out the mass of the moving object when finding energy.

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