IB Physics SLTopic A.3 — Work, Energy & PowerPaper 1 & 2Conservation of Energy~7 min read
Conservation of Energy
Energy is never created and never destroyed — it just moves between stores or changes form. This idea sits underneath almost every calculation in this topic, so it’s worth getting comfortable with it before the equations start piling up.
📘 What you need to know
The total energy of an isolated system never changes — only how that energy is distributed between different stores can change
A “system” is simply whatever object or group of objects you’ve chosen to focus on; everything else is the surroundings
No real energy transfer is 100% efficient — some energy always ends up spread out as thermal energy in the surroundings
Energy that ends up somewhere unhelpful is called wasted energy, not “lost” energy — it still exists, it’s just no longer useful
Sankey diagrams give a visual, to-scale breakdown of useful versus wasted energy in a process
Systems, Surroundings and Why They Matter
In physics, a system is just the object — or group of objects — that you’ve decided to analyse. Drawing a boundary around a system lets you ignore everything outside it and focus only on the energy stores that are actually relevant to the problem in front of you.
When a system is in equilibrium, nothing is changing, so there’s nothing to track. It’s only when something in the system changes — a ball starts falling, a spring is released, a motor switches on — that energy gets transferred, and that’s exactly when conservation of energy becomes useful.
The Stores You’ll Meet Most Often
Kinetic — held by anything that’s moving
Gravitational potential — held by anything raised up in a gravitational field
Elastic potential — held by anything stretched or compressed, like a spring
Chemical — held within bonds, e.g. in a battery or fuel
Internal (thermal) — linked to the temperature of an object
Nuclear — held within the nucleus of an atom
Kinetic, gravitational potential and elastic potential energy are grouped together as mechanical energy — these three are the ones you’ll juggle constantly in this topic.
Where Does “Wasted” Energy Actually Go?
Every time energy is transferred from one store to another, some of it escapes to the surroundings in a form that’s hard to make use of again — almost always as thermal energy. That escaping portion is described as dissipated or wasted energy. It hasn’t vanished; conservation of energy guarantees it’s still out there somewhere. It’s simply no longer doing the job you wanted it to do.
Take a phone charger: electrical energy goes in, and most of it is transferred usefully into the chemical store of the battery — but some inevitably ends up heating the charger casing and the surrounding air instead. That warmth is wasted energy.
The width of each arrow is proportional to the amount of energy it carries — total energy in always equals useful output plus wasted energy
Sankey Diagrams: Reading the Arrows
The rules of a Sankey diagram
The arrow’s width is drawn to scale — it directly represents the amount of energy flowing along it
The branch that keeps travelling in the original direction represents the useful energy output
Any branch that peels off (usually drawn heading downward) represents wasted energy
A device with a narrower “wasted” branch is doing a better job — it’s wasting less energy for the same input
Conservation of energy, in one line
Total energy in = Useful energy out + Wasted energy
Conservation of Energy in Mechanical Systems
Whenever a system is dominated by kinetic, gravitational potential and elastic potential stores — a falling object, a pendulum, a mass on a spring — conservation of energy shows up as one store’s loss being another store’s gain. If resistive forces such as friction or air resistance are doing work too, that work also has to be accounted for.
For an object sliding up a rough slope, for example:
Loss in kinetic energy = Gain in gravitational potential energy + Work done against friction
🧭 Recipe: Solving a Conservation-of-Energy Problem
Identify the stores — decide which energy stores are increasing and which are decreasing
Write the conservation statement — “loss = gain” for a purely mechanical system, or “total in = useful out + wasted” if efficiency is involved
Substitute expressions — swap in mgh for gravitational potential energy, ½mv² for kinetic energy, ½k(Δx)² for elastic potential energy, wherever they apply
Solve for the unknown — rearrange and calculate, keeping an eye on units throughout
Quick recap: Energy is never destroyed — it only moves between stores. Total energy in always equals useful energy out plus wasted energy, whether you’re analysing a falling ball or an electric motor.
WE 1
An electric kettle is rated to draw 800 J of electrical energy while it operates. Of this, 560 J is usefully transferred to the internal energy store of the water. How much energy is wasted?
Step 1 — State conservation of energy
Total energy in = Useful energy out + Wasted energy
Step 2 — Rearrange for wasted energy
Wasted energy = Total energy in − Useful energy out
Step 3 — SubstituteWasted energy = 800 − 560= 240 J
WE 2
A 52 kg skateboarder starts from rest at the top of a ramp and descends through a vertical height of 3.2 m. Air resistance and friction dissipate 18% of the gravitational potential energy lost. Calculate the skateboarder’s speed at the bottom of the ramp.
Step 1 — Find the GPE lostΔE_p = mgh = 52 × 9.8 × 3.2 ≈ 1630 JStep 2 — Find the KE gained
Only 82% of the GPE lost becomes kinetic energy
E_k = 0.82 × 1630 ≈ 1340 JStep 3 — Solve for speedE_k = ½mv² → v = √(2E_k ÷ m) = √(2 × 1340 ÷ 52)v ≈ 7.2 m s⁻¹Note: only the fraction that becomes kinetic energy goes into the ½mv² equation — not the full GPE lost.
💡 Top tips
Always pin down your system first — it decides exactly what counts as “in” and what counts as “out”
Read a Sankey diagram’s arrow widths like a scale, not just a picture — the numbers matter as much as the shape
“Wasted” energy is still energy — never subtract it as if it disappeared from the universe, only from the useful total
Decide up front whether a question needs loss = gain or total in = useful out + wasted — they’re the same principle, just phrased for different situations
⚠ Common mistakes
Multiplying an efficiency percentage by the wrong store — it applies to the starting store, not the one you’re solving for
Assuming a falling or sliding object has no dissipation unless a resistive force is explicitly mentioned in the question
Confusing power with energy — power is the rate of energy transfer, not the total amount transferred
Treating a device’s “useful” output as automatically 100% of the input — always check what fraction the question actually gives you
Up next: Work Done — where we turn today’s energy language into the W = Fs equation you’ll use in almost every calculation from here on.
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