IB Physics Topic 1.3: Work, energy and power | Notes & Flashcards

IB Physics — Work, energy and power

Topic 1.3 of IB Physics covers Work, energy and power, which is part of Unit 1: Space, time and motion. Students explore key concepts including Work done & force-distance graphs, Kinetic energy & the work-energy principle, Gravitational PE & conservation of energy, and more. A strong understanding of work, energy and power is essential for IB Physics exams and builds the foundation for connected topics across the syllabus.

Key concepts in Work, energy and power

Key Idea: This topic is the energy toolkit: forces do work, which is stored as kinetic, gravitational or elastic energy, transferred at a rate set by power, and never destroyed — only shared out and partly wasted as heat.

Do work

W = Fs cos θ: only the part of F along the motion
Area under a force–distance graph = work
Work by the resultant force = change in kinetic energy

Store it

Kinetic ½mv², gravitational mgΔh, elastic ½kΔx²
Mechanical energy = their sum
No friction: mechanical energy is conserved

Use it

Power P = ΔW/Δt = Fv
Efficiency = useful out ÷ total in
Sankey diagrams; energy density of fuels (J m⁻³)

It is examined on both papers: quick definition and 'double the speed' MCQs on Paper 1A, and multi-step calculations (force–distance areas, slide-to-rest, falling-body speeds, spring collisions, power against drag, efficiency) on Paper 2.

The six given equations

Every equation below is given in the data booklet (Theme A.3) — tap any one for the booklet entry. Knowing which to reach for is the skill, so the table after them sorts that out.

\begin{aligned} W = Fs\cos\theta \\ E_k = \tfrac{1}{2}mv^{2} = \frac{p^{2}}{2m} \\ \Delta E_p = mg\,\Delta h \\ E_H = \tfrac{1}{2}k\,\Delta x^{2} \\ P = \frac{\Delta W}{\Delta t} = Fv \\ \eta = \frac{\text{useful out}}{\text{total in}} \end{aligned}

Work done by a force. When the force is along the motion θ = 0 and cos 0 = 1, so W = Fs. Kinetic energy — ½mv² when you know the speed, p²/2m when you know the momentum. Change in gravitational PE — equal to the kinetic energy gained in a free fall. Elastic potential energy stored in a stretched or squashed spring. Convert any cm to m before squaring Δx. Power. Use ΔW/Δt with energy and time; use Fv when a force moves at a steady speed (e.g. cruising against drag). Efficiency — the useful fraction of the energy (or power) supplied. Always between 0 and 1; × 100 for a %.

$W$: work done = energy transferred (J)
$F$: force applied (N)
$s$: distance moved (m)
$\theta$: angle between the force and the direction of motion (°)
$E_k$: kinetic energy — the energy of motion (J)
$m$: mass (kg)
$v$: speed (m s⁻¹)
$p$: momentum, p = mv (kg m s⁻¹)
$\Delta E_p$: change in gravitational PE (J)
$g$: gravitational field strength (≈ 9.8 N kg⁻¹ on Earth)
$\Delta h$: change in height (m)
$E_H$: elastic potential energy stored in the spring (J)
$k$: spring constant — the stiffness (N m⁻¹)
$\Delta x$: extension or compression from the natural length (m)
$P$: power — energy transferred per second (W = J s⁻¹)
$\Delta W$: work done / energy transferred (J)
$\Delta t$: time taken (s)
$\eta$: efficiency — the useful fraction (0 to 1; × 100 for a %), no unit
$\text{useful out}$: useful work or power that comes out (J or W)
$\text{total in}$: total work or power put in (J or W)

Which one when?

You're told…	Use	Watch out for
a force pushing through a distance	W = Fs cos θ	θ is between the force and the motion; force across the motion (90°) does no work
a force–distance graph	area under the line = work	rectangle for a flat line, triangle for a sloping spring line — the area is energy (J), not a speed
mass and speed (or momentum)	Eₖ = ½mv² (or p²/2m)	square the speed; double v → four times the energy
a change of height	ΔEₚ = mgΔh	use the vertical rise only; the mass cancels when you set mgΔh = ½mv²
a spring's stiffness and stretch	EH = ½kΔx²	square Δx and convert cm → m first
energy (or work) and time	P = ΔW/Δt	answer is in watts (J s⁻¹)
a steady speed against a resistive force	P = Fv	F here is the resistive (drag) force, since the speeds aren't changing
useful vs total energy	η = useful ÷ total	always ≤ 1; over 100% means you swapped 'useful' and 'total'
a ramp or a pendulum	h = L sin θ or h = L(1 − cos θ)	mgΔh needs the vertical height, never the ramp or string length
a fuel's energy and its volume	energy density = E ÷ V (J m⁻³)	per kilogram it is the specific energy (J kg⁻¹)

Conservation, transfers & waste

Idea	What it says	Typical use
Work–energy principle	net work done = change in kinetic energy (Wₙₑₜ = ΔEₖ)	a push speeds an object up; friction does negative work that removes Eₖ → slide-to-rest distance
Conservation of energy	for a free fall (no air resistance) PE lost = KE gained → mgΔh = ½mv²	landing speeds, pendulum swing speeds — the mass cancels
Energy transfer / degradation	energy is never lost, only moved — the wasted branch is almost always thermal energy (heat)	Sankey accounting: useful + wasted branches add up to the input
With friction	PE lost = KE gained + work against friction	rough ramp: Eₖ at the bottom = mgh − Fd; the lost energy is thermal

When something slides to a stop, friction takes away all its kinetic energy: friction force × distance = Eₖ, so distance = Eₖ ÷ friction force.

IB-style worked examples

IB-style questionDetermine[4 marks]

A 3.0 kg trolley starts from rest on a smooth track. A constant net force of 12 N acts on it as it moves 5.0 m, shown on a force–distance graph. (a) State what the area under the graph represents. (b) Find the trolley's final speed.

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IB-style questionDetermine[3 marks]

A 0.60 kg ball falls from rest through a height of 2.0 m. Air resistance is negligible and g = 9.8 N kg⁻¹. Find its speed just before it lands.

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IB-style questionDetermine[4 marks]

A van cruises at a steady 20 m s⁻¹ against a total resistive force of 600 N. (a) Find the useful power the van delivers to overcome drag. (b) The engine is supplied with 18 kW of power. Find its efficiency.

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Important: With friction, mechanical energy is not conserved: PE lost = KE gained + friction × distance along the path. The missing energy becomes thermal energy.

Quick self-check

Tap each card to reveal the answer.

A force acts at 90° to the motion — how much work does it do? Zero — cos 90° = 0, so W = Fs cos θ = 0 (e.g. the normal force on a sliding block).

You double an object's speed — what happens to its kinetic energy? It becomes four times as big, because the speed is squared (2² = 4).

Does a falling object's landing speed depend on its mass? No — in mgΔh = ½mv² the mass cancels, so heavy and light objects reach the same speed (no air resistance).

How does the energy stored in a spring change if you stretch it twice as far? It becomes four times as big — EH = ½kΔx² has the stretch squared.

What is the power of a vehicle cruising at constant speed? P = Fv, where F is the resistive (drag) force the engine has to balance.

Where does the 'wasted' energy in a machine usually go? Almost always to thermal energy (heat) — it isn't destroyed, just spread out and made useless.

Exam tips

Pick the equation from what you're GIVEN: force × distance → W = Fs cos θ; mass & speed → Eₖ = ½mv²; height → ΔEₚ = mgΔh; spring stretch → EH = ½kΔx²; energy & time (or steady-speed force) → P; useful vs total → η.
Area under a force–distance graph = the work done — a rectangle for a flat line, a triangle for a sloping spring line. The area is energy in joules, not a speed.
Always square the variable that's squared: v in ½mv² and Δx in ½kΔx². Double it → four times the energy (the classic 'stopping distance' point).
Conservation of energy: set PE lost = KE gained → mgΔh = ½mv²; the mass cancels, so don't carry it through.
Slide-to-rest against friction: friction force × distance = Eₖ, so distance = Eₖ ÷ friction force.
At constant speed use P = Fv with F as the resistive force; convert kW ↔ W and cm ↔ m before substituting.
Efficiency is a fraction ≤ 1 — if you get more than 100%, you've divided total by useful instead of useful by total.

IB Physics — Work, energy and power

Key concepts in Work, energy and power

Key Idea: This topic is the energy toolkit: forces do work, which is stored as kinetic, gravitational or elastic energy, transferred at a rate set by power, and never destroyed — only shared out and partly wasted as heat.

Do work

W = Fs cos θ: only the part of F along the motion
Area under a force–distance graph = work
Work by the resultant force = change in kinetic energy

Store it

Kinetic ½mv², gravitational mgΔh, elastic ½kΔx²
Mechanical energy = their sum
No friction: mechanical energy is conserved

Use it

Power P = ΔW/Δt = Fv
Efficiency = useful out ÷ total in
Sankey diagrams; energy density of fuels (J m⁻³)

The six given equations

Every equation below is given in the data booklet (Theme A.3) — tap any one for the booklet entry. Knowing which to reach for is the skill, so the table after them sorts that out.

\begin{aligned} W = Fs\cos\theta \\ E_k = \tfrac{1}{2}mv^{2} = \frac{p^{2}}{2m} \\ \Delta E_p = mg\,\Delta h \\ E_H = \tfrac{1}{2}k\,\Delta x^{2} \\ P = \frac{\Delta W}{\Delta t} = Fv \\ \eta = \frac{\text{useful out}}{\text{total in}} \end{aligned}

$W$: work done = energy transferred (J)
$F$: force applied (N)
$s$: distance moved (m)
$\theta$: angle between the force and the direction of motion (°)
$E_k$: kinetic energy — the energy of motion (J)
$m$: mass (kg)
$v$: speed (m s⁻¹)
$p$: momentum, p = mv (kg m s⁻¹)
$\Delta E_p$: change in gravitational PE (J)
$g$: gravitational field strength (≈ 9.8 N kg⁻¹ on Earth)
$\Delta h$: change in height (m)
$E_H$: elastic potential energy stored in the spring (J)
$k$: spring constant — the stiffness (N m⁻¹)
$\Delta x$: extension or compression from the natural length (m)
$P$: power — energy transferred per second (W = J s⁻¹)
$\Delta W$: work done / energy transferred (J)
$\Delta t$: time taken (s)
$\eta$: efficiency — the useful fraction (0 to 1; × 100 for a %), no unit
$\text{useful out}$: useful work or power that comes out (J or W)
$\text{total in}$: total work or power put in (J or W)

Which one when?

You're told…	Use	Watch out for
a force pushing through a distance	W = Fs cos θ	θ is between the force and the motion; force across the motion (90°) does no work
a force–distance graph	area under the line = work	rectangle for a flat line, triangle for a sloping spring line — the area is energy (J), not a speed
mass and speed (or momentum)	Eₖ = ½mv² (or p²/2m)	square the speed; double v → four times the energy
a change of height	ΔEₚ = mgΔh	use the vertical rise only; the mass cancels when you set mgΔh = ½mv²
a spring's stiffness and stretch	EH = ½kΔx²	square Δx and convert cm → m first
energy (or work) and time	P = ΔW/Δt	answer is in watts (J s⁻¹)
a steady speed against a resistive force	P = Fv	F here is the resistive (drag) force, since the speeds aren't changing
useful vs total energy	η = useful ÷ total	always ≤ 1; over 100% means you swapped 'useful' and 'total'
a ramp or a pendulum	h = L sin θ or h = L(1 − cos θ)	mgΔh needs the vertical height, never the ramp or string length
a fuel's energy and its volume	energy density = E ÷ V (J m⁻³)	per kilogram it is the specific energy (J kg⁻¹)

Conservation, transfers & waste

Idea	What it says	Typical use
Work–energy principle	net work done = change in kinetic energy (Wₙₑₜ = ΔEₖ)	a push speeds an object up; friction does negative work that removes Eₖ → slide-to-rest distance
Conservation of energy	for a free fall (no air resistance) PE lost = KE gained → mgΔh = ½mv²	landing speeds, pendulum swing speeds — the mass cancels
Energy transfer / degradation	energy is never lost, only moved — the wasted branch is almost always thermal energy (heat)	Sankey accounting: useful + wasted branches add up to the input
With friction	PE lost = KE gained + work against friction	rough ramp: Eₖ at the bottom = mgh − Fd; the lost energy is thermal

When something slides to a stop, friction takes away all its kinetic energy: friction force × distance = Eₖ, so distance = Eₖ ÷ friction force.

IB-style worked examples

IB-style questionDetermine[4 marks]

Model answer plan

See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.

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IB-style questionDetermine[3 marks]

A 0.60 kg ball falls from rest through a height of 2.0 m. Air resistance is negligible and g = 9.8 N kg⁻¹. Find its speed just before it lands.

Model answer plan

See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.

Claim your free topic →

IB-style questionDetermine[4 marks]

Model answer plan

See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.

Claim your free topic →

Important: With friction, mechanical energy is not conserved: PE lost = KE gained + friction × distance along the path. The missing energy becomes thermal energy.

Quick self-check

Tap each card to reveal the answer.

A force acts at 90° to the motion — how much work does it do? Zero — cos 90° = 0, so W = Fs cos θ = 0 (e.g. the normal force on a sliding block).

You double an object's speed — what happens to its kinetic energy? It becomes four times as big, because the speed is squared (2² = 4).

Does a falling object's landing speed depend on its mass? No — in mgΔh = ½mv² the mass cancels, so heavy and light objects reach the same speed (no air resistance).

How does the energy stored in a spring change if you stretch it twice as far? It becomes four times as big — EH = ½kΔx² has the stretch squared.

What is the power of a vehicle cruising at constant speed? P = Fv, where F is the resistive (drag) force the engine has to balance.

Where does the 'wasted' energy in a machine usually go? Almost always to thermal energy (heat) — it isn't destroyed, just spread out and made useless.

Exam tips

Pick the equation from what you're GIVEN: force × distance → W = Fs cos θ; mass & speed → Eₖ = ½mv²; height → ΔEₚ = mgΔh; spring stretch → EH = ½kΔx²; energy & time (or steady-speed force) → P; useful vs total → η.
Area under a force–distance graph = the work done — a rectangle for a flat line, a triangle for a sloping spring line. The area is energy in joules, not a speed.
Always square the variable that's squared: v in ½mv² and Δx in ½kΔx². Double it → four times the energy (the classic 'stopping distance' point).
Conservation of energy: set PE lost = KE gained → mgΔh = ½mv²; the mass cancels, so don't carry it through.
Slide-to-rest against friction: friction force × distance = Eₖ, so distance = Eₖ ÷ friction force.
At constant speed use P = Fv with F as the resistive force; convert kW ↔ W and cm ↔ m before substituting.
Efficiency is a fraction ≤ 1 — if you get more than 100%, you've divided total by useful instead of useful by total.

IB Physics — Work, energy and power

Key concepts in Work, energy and power

The six given equations

Which one when?

Conservation, transfers & waste

IB-style worked examples

Quick self-check

Exam tips

Exam tips

What you'll learn in Topic 1.3

Study resources — 1.3 Work, energy and power

Work done & force-distance graphs

Kinetic energy & the work-energy principle

Gravitational PE & conservation of energy

Elastic potential energy

Power & efficiency

Energy in collisions & systems (Sankey/energy transfers)

Ready to study Work, energy and power?

Ready to practice?

IB Physics — Work, energy and power

Key concepts in Work, energy and power

The six given equations

Which one when?

Conservation, transfers & waste

IB-style worked examples

Quick self-check

Exam tips

Exam tips

What you'll learn in Topic 1.3

Study resources — 1.3 Work, energy and power

Work done & force-distance graphs

Kinetic energy & the work-energy principle

Gravitational PE & conservation of energy

Elastic potential energy

Power & efficiency

Energy in collisions & systems (Sankey/energy transfers)

Ready to study Work, energy and power?

Ready to practice?