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Theme A — Space, Time and Motion

A.3 Work, Energy and Power — IB Physics SL Revision Notes & Topical Questions

5 min read 10 parts Lesson 30 of 41 1 quiz

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Lesson summary

A.3 Work, Energy and Power — IB SL Notes — IB PHYSICS SL notes: Use work, the conservation of energy, power and efficiency to analyse mechanical energy transfers, and interpret energy density and Sankey diagrams.Work done — W = Fs cos θ, the energy transferred by a force.θ is the…

  • Perpendicular force
  • Varying force
  • Dissipation
  • Work–energy theorem
  • Gravitational potential
  • Elastic potential

Part 1 of 8Work

Work done
  • W = Fs cos θ, the energy transferred by a force.
  • θ is the angle between the force and the displacement.
  • The unit is the joule, 1 J = 1 N m.
Perpendicular force
  • Perpendicular force it does no work.
Varying force
  • Varying force the work is the area under the force–displacement graph.

Part 2 of 8Conservation of energy

Principle
  • Principle energy cannot be created or destroyed, only transferred or transformed.
Dissipation
  • Dissipation no transfer is 100% efficient, and the wasted energy usually becomes thermal energy of the surroundings.
Work–energy theorem
  • Work–energy theorem the net work done on a body equals its change in kinetic energy.

Part 3 of 8Energy stores in mechanics

StoreEquationDepends on
KineticEk = ½mv2 = p2/2mMass and speed
Gravitational potentialΔEp = mgΔhMass, field strength, height change
Elastic potentialEH = ½k(Δx)2Spring constant and extension
Gravitational potential
  • Gravitational potential only changes matter, and the zero level is a free choice.
Elastic potential
  • Elastic potential it equals the area under the force–extension line for a spring obeying Hooke's law.

Part 4 of 8Mechanical energy

Mechanical energy
  • Mechanical energy the sum Ek + Ep + EH.
No resistive forces
  • No resistive forces mechanical energy is conserved.
With resistive forces
  • With resistive forces work done against them equals the mechanical energy transferred to thermal energy.

Part 5 of 8Power and efficiency

Power
  • P = ΔW/Δt, with unit the watt, 1 W = 1 J s−1.
Steady motion
  • Steady motion for a constant driving force at constant velocity, P = Fv.
Efficiency
  • η = useful output / total input, for energy or power.
  • It has no unit and is below 1 for real machines.

Part 6 of 8Sankey diagrams and energy density

Sankey diagram
  • Sankey diagram the width of each arrow is proportional to the energy or power it represents.
  • Total energy in = useful energy out + wasted energy.
Energy density
  • Energy density the energy released per unit volume of fuel, in J m−3.
Specific energy
  • Specific energy the energy per unit mass of fuel.

Part 7 of 8Solving energy problems

1
Identify the system and the initial and final states.
2
List the energy stores at each state: kinetic, gravitational and elastic.
3
Write initial total energy = final total energy + work done against resistive forces.
4
Solve for the unknown and check the units.

Part 8 of 8More from the specification

More from the specification
Work done against resistive forces
  • Work done against resistive forces integrating applied mechanical force along displacement paths provides an analytical means to evaluate expended work.
Work Done by a Force at an Angle
  • Work done on an object is calculated as W = F * s * cos(theta),
  • where only the component of force acting parallel to the direction of displacement along the horizontal or vertical axis performs mechanical work.
Dissipative Forces and Friction
  • When an object slides across a rough surface, friction opposes motion and dissipates mechanical energy into thermal energy,
  • meaning the total amount of mechanical work input exceeds useful kinetic or potential energy gained.
Gravitational Potential Energy and Position
  • The gravitational potential energy stored in an object or a mass of water depends on its vertical position in a gravitational field, calculated using Delta Ep = m * g * Delta h.
Power Output of an Electric Motor
  • Power is defined as the rate of energy transfer or work done; the useful power of an electric motor pumping water or lifting a load reflects electrical power minus internal dissipated losses.
    • (P = W / Delta t = F * v)
Friction
  • Force parallel to the surface opposing relative motion or its tendency.
Component
  • Part of a vector along one axis.
Position
  • Location relative to a reference point.
Distance
  • Total length of path travelled, a scalar.
Resultant force
  • Another name for net force.
W
Fs = 25.6 × 20 = 512 J
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)

Key terms

TermMeaning
Work doneThe product of the force and the displacement in the direction of the force
Kinetic energyThe energy a body has because of its motion
Gravitational potential energyThe energy a body has because of its position in a gravitational field
Elastic potential energyThe energy stored in a deformed elastic object
PowerThe rate at which work is done or energy is transferred
EfficiencyThe ratio of useful output energy (or power) to total input energy (or power)
Energy densityThe energy released per unit volume of a fuel

Avoid these mistakes

1
Counting a force perpendicular to the motion as doing work — only the component along the displacement does work.
2
Using mechanical energy conservation when friction acts — include the energy dissipated.
3
Using P = Fv when velocity is not constant — it applies to constant force at constant velocity (or instantaneous values).
4
Writing efficiency with a unit — it is a ratio.
5
Mixing joules and kilowatt-hours — 1 kW h = 3.6 × 106 J.

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