🟢 Energy · Class 9–11 · Boards + AP + Olympiad

Nothing is ever lost — only changed

Conservation of energy · kinetic & potential energy · energy transformations · mechanical energy · efficiency

Drop a ball and it speeds up; let a pendulum swing and it climbs back to the same height. Energy is never made or destroyed — it just changes form. Stored height energy becomes motion, motion becomes heat, but the total never changes. That single idea — energy is conserved — runs through every machine, every roller coaster, and every meal you eat.

Energy · measured in joulesKE = ½mv² · energy of motionPE = mgh · stored by heightTotal · never changes
What you'll learn

Conservation of Energy — the rule behind everything

This page covers the law of conservation of energy — energy is never created or destroyed, only changed in form — together with kinetic energy (½mv²), potential energy (mgh), mechanical energy, energy transformations and efficiency. By the end you'll be able to:

  • State the law and explain why the total energy never changes.
  • Calculate kinetic energy (½mv²) and potential energy (mgh).
  • Use energy conservation to find a speed from a drop height (v = √(2gh)).
  • Track energy transformations through a device or a falling ball.
  • Work out efficiency and explain where the "wasted" energy really goes.
Why it matters · where it's tested

The most universal law in physics

Every roller coaster, power station, engine and living cell obeys it — and "Work and Energy" is one of the most-tested chapters at every level. We go beyond the syllabus, but we never skip it:

CBSE · Class 9 — Work and Energy CBSE · Class 11 — Work, Energy & Power ICSE / NCERT IGCSE · Cambridge / Edexcel — Energy AP Physics 1 — Energy Olympiad — NSO · NSEJS · IPhO foundations

Searched as: law of conservation of energy, kinetic and potential energy, energy transformations, ½mv², mgh, efficiency.

See it live

Set the drop height and mass, then watch the ball trade height for speed — potential and kinetic energy swap while the total stays flat. Switch on friction to see energy leak away as heat. 🟢 real energy engine

Energy playground

Height2 m
Mass1 kg
Total energy20 J
Speed (bottom)6.3 m/s
Track
E = mgh = 1 × 9.8 × 2 = 20 J

Set a drop height and mass to see what they mean.

What's going on

In plain terms: energy comes in forms — motion (kinetic) and stored (potential) among them — and as they swap, the total stays the same.

What it is

Energy is the capacity to do work, and it wears many coats. A moving object carries kinetic energy, KE = ½mv²; a raised or stretched one stores potential energy, like gravitational PE = mgh. Heat, light, sound, chemical and electrical energy are forms too. The law of conservation of energy says you can pour energy from one form into another freely — but you can never make a drop of it from nothing, nor make a drop vanish.

How the principle works

Watch a ball on a frictionless track: at the top it is still and high — all potential energy. Let go and it speeds up as that PE turns into kinetic energy, fastest at the bottom where the height is least. Up the far side it slows and climbs back to the same height, KE turning into PE again. At every instant KE + PE is the same — its mechanical energy is conserved. Add friction and that mechanical energy slowly drains into heat, but the grand total, heat included, is still unchanged.

How it works in the playground

The playground above drops a ball on a valley track. The Scene tab shows it swinging and reports its live KE and PE; the Energy bars tab shows KE and PE as two bars that breathe in and out while the dashed Total bar holds its height. Flip on friction and a Heat bar grows as the swing dies down — the total still level, proof that nothing is lost. Slide the height or mass and the starting energy (E = mgh) changes with it. 🟡 maths of the picture

Edge cases
  • No friction → mechanical energy (KE + PE) is conserved; the ball returns to its start height.
  • With friction → mechanical energy falls, but heat rises by the same amount; the total is still conserved.
  • Energy is never destroyed — "lost" energy has become heat spread into the surroundings.
  • Speed depends on drop height, not mass — v = √(2gh); the mass cancels out.
Three points & measures
  • Kinetic energy (J) — ½mv²; the energy of motion.
  • Potential energy (J) — mgh; energy stored by height.
  • Total energy (J) — KE + PE (+ heat); the number that never changes.

Solve it with me, step by step 🟢 Class 9

Exams reward the method, not just the answer. Work it out one step at a time — read the thought, predict the line, then reveal it. Switch to practice to type your own numbers and check them.

See the maths

The physics is visible in the diagram; the maths usually hides. These little labs make it visible too — drag a slider and watch the numbers and arrows answer.

🔢 KE & PE Calculator

Two formulas, side by side. Drag the mass, speed and height and watch kinetic energy (½mv²) and potential energy (mgh) rise and fall.
Kinetic
9.0 J
Potential
19.6 J
KE = ½mv² = 9.0 J · PE = mgh = 19.6 J

📐 Speed From a Drop

Set a drop height and energy conservation gives the landing speed: mgh becomes ½mv², so v = √(2gh) — and the mass cancels out. Add friction and some energy leaks to heat.
Drop
5 m
Speed
9.9 m/s
v = √(2gh) = √(2·9.8·5) = 9.9 m/s

⚙️ Efficiency & Where Energy Goes

A machine takes in energy and gives some out useful — the rest becomes heat. The input arrow splits, but the two halves always add back to the whole: energy is conserved, just degraded.
Efficiency
70%
efficiency = useful ÷ total = 70 ÷ 100 = 70% (the rest, 30 J, becomes heat)

In the real world

The roller coaster

The first hill is the highest because that is where all the energy is stored. Plunging down, that height energy (PE) turns into speed (KE); climbing the next hill turns it back. A little leaks to friction each time, so every hill is lower than the last.

A hydroelectric dam

Water held high behind a dam stores gravitational potential energy. Released, it rushes down and spins turbines — PE becomes kinetic energy becomes the electrical energy in the wires. Nothing is created; the sun's energy that lifted the water as rain is simply cashed in.

A bouncing ball

Each bounce, a ball returns a little lower. The "missing" energy isn't gone — it became heat and a tiny sound on every impact. Add it all up and the total energy is exactly what you started with; it has just spread out where you can't use it.

Build it yourself — science-fair projects

Physics you can hold. Each project below demonstrates a law you just met — and the measuring is what turns a demo into a science-fair winner. Pick one, build it from things at home, and graph something.

🎡Beginner

The pendulum that never cheats

Shows · conservation of energy

Build: hang a heavy nut on a string, hold it to the tip of your nose and let go — it swings out and back but never quite reaches your nose.

Measure: release height vs return height — it never exceeds where it started, because energy can't be created.

🏎️Beginner

Marble ramp

Shows · PE → KE

Build: roll a marble down a ramp from different heights into a small cup it has to shove along the table.

Measure: how far it pushes the cup vs the drop height — more height stores more energy, so a bigger push.

🪀Intermediate

Rubber-band car

Shows · elastic PE → KE

Build: wind a rubber band around an axle to drive a small cardboard car; the wound band stores elastic energy.

Measure: distance travelled vs number of winds — more stored elastic energy means it goes further.

Intermediate

Bounce-height tester

Shows · energy "loss" to heat

Build: drop a ball from a fixed height beside a ruler and read each rebound height.

Measure: rebound ÷ drop = the fraction of energy kept; compare a tennis ball, a super-ball and a beanbag.

💧Intermediate

Water-wheel generator

Shows · PE → KE → electrical

Build: pour water onto a foil or cork wheel that spins a tiny hobby motor as a generator, wired to an LED.

Measure: LED brightness vs how high you pour from — more height, more energy, more light.

☀️Champion

Solar oven

Shows · light → heat & efficiency

Build: line a box with foil and add a clear lid; aim it at the sun to warm a small cup of water or a snack.

Measure: the temperature rise over time, and estimate the efficiency — how much sunlight became useful heat.

Glossary — the 10 words that unlock it

Energy

What it means
The capacity to do work; it comes in many forms and is measured in joules.
Why it matters
Almost everything that happens is energy moving or changing form.
Example
A moving car, a hot drink and a charged battery all hold energy.
Key question
Can energy ever be created from nothing?

Kinetic energy

What it means
The energy of a moving object, equal to ½mv².
Why it matters
It is what does the damage in a collision and the work in a moving machine.
Example
A 2 kg ball at 3 m/s has ½ × 2 × 3² = 9 J.
Key question
What happens to KE if the speed doubles?

Potential energy

What it means
Stored energy of position or state; gravitational PE is mgh.
Why it matters
It is the energy waiting to be released — by falling, unwinding or stretching back.
Example
A 1 kg book on a 2 m shelf stores about 20 J.
Key question
Where does a raised object's PE go when it falls?

Mechanical energy

What it means
The sum of an object's kinetic and potential energy.
Why it matters
It stays constant when only gravity acts, which makes problems easy to solve.
Example
A swinging pendulum keeps the same KE + PE throughout (no friction).
Key question
What makes mechanical energy stop being conserved?

Conservation of energy

What it means
Energy is never created or destroyed; it only changes form, so the total stays constant.
Why it matters
It lets you account for energy from start to finish, even through messy changes.
Example
A falling ball's PE becomes KE, then heat and sound on impact.
Key question
If a machine seems to lose energy, where did it go?

Energy transformation

What it means
The change of energy from one form to another.
Why it matters
Every device is really an energy converter.
Example
A torch turns electrical energy into light (and some heat).
Key question
What does a solar panel transform, and into what?

Joule

What it means
The SI unit of energy (J) — the work done by a one-newton force over one metre.
Why it matters
It lets us compare energies of every kind on one scale.
Example
Lifting an apple about one metre takes roughly one joule.
Key question
Why do food labels show thousands of joules?

Work

What it means
Energy transferred when a force moves something; work = force × distance.
Why it matters
It is how energy gets moved from place to place and store to store.
Example
Pushing a box 3 m with 10 N does 30 J of work.
Key question
Is work done if the object does not move?

Efficiency

What it means
The fraction of input energy that comes out useful: useful output ÷ total input.
Why it matters
It tells you how much energy a device wastes as heat.
Example
A lamp giving 12 J of light from 60 J is 20% efficient.
Key question
Why can no machine ever be 100% efficient?

Dissipation

What it means
The spreading of useful energy into heat in the surroundings.
Why it matters
It is where "lost" energy actually goes — conserved, but no longer useful.
Example
Brakes turn a car's kinetic energy into heat in the discs.
Key question
Why is dissipated heat so hard to reuse?

The questions people ask

Energy runs through every machine and every motion. Here are the questions that come up most — each answer reads on its own, lifted clean off the page.

What is the law of conservation of energy?
ConceptualWhatcomplexity 2

The law of conservation of energy states that energy cannot be created or destroyed; it can only be changed from one form to another. So the total amount of energy in a closed system stays constant. When a ball falls, its potential energy turns into kinetic energy; when it lands, that becomes heat and sound — but at every stage the total energy is the same. It is one of the most thoroughly tested rules in all of physics.

What is the difference between kinetic and potential energy?
ComparativeWhatcomplexity 2
FeatureKinetic energyPotential energy
What it isEnergy of motionStored energy of position or state
FormulaKE = ½mv²Gravitational PE = mgh
Depends onMass and speed²Mass, gravity and height
ExampleA speeding carA raised hammer
Is energy ever really destroyed?
ConceptualWhycomplexity 3

No, energy is never really destroyed. When energy seems to be lost — for example to friction or air resistance — it has actually been converted into heat (and sometimes sound) that spreads out into the surroundings. The total energy is still exactly the same; it has just changed into a more scattered, less useful form. This is why no machine can ever be perfectly efficient: some energy always ends up as waste heat.

What is mechanical energy and when is it conserved?
ConceptualWhatcomplexity 3

Mechanical energy is the sum of an object's kinetic energy and potential energy. It is conserved — stays constant — when the only force doing work is gravity (or another conservative force) and there is no friction or air resistance. On a frictionless slide or a swinging pendulum, kinetic and potential energy trade back and forth while their total is unchanged. Once friction acts, mechanical energy falls because some of it turns into heat.

How do you calculate kinetic and potential energy?
How-ToHowcomplexity 3

Kinetic energy is calculated as KE = ½mv², where m is the mass in kilograms and v is the speed in metres per second; the answer is in joules. Gravitational potential energy is PE = mgh, where g is about 9.8 m/s² and h is the height in metres. For example, a 2 kg ball at 3 m/s has KE = ½ × 2 × 3² = 9 J, and lifted 5 m it has PE = 2 × 9.8 × 5 = 98 J.

What is efficiency and why is no machine 100% efficient?
ConceptualWhycomplexity 3

Efficiency is the fraction of the input energy that comes out as useful energy: efficiency = useful output ÷ total input, written as a percentage. No machine is 100% efficient because some energy is always dissipated as heat through friction, air resistance or electrical resistance. For example, a lamp that takes in 60 J and gives out 12 J of light is 20% efficient; the other 48 J becomes heat — conserved, but no longer useful as light.

What are some everyday energy transformations?
ApplicationWhatcomplexity 2

Everyday energy transformations are everywhere: a torch turns electrical energy into light, a loudspeaker turns electrical energy into sound, a battery turns chemical energy into electrical energy, and a solar panel turns light into electrical energy. When you eat, chemical energy in food becomes the kinetic energy of your moving muscles and heat. In every case the form changes but the total energy is conserved.

How does a roller coaster show conservation of energy?
ScenarioHowcomplexity 3

A roller coaster shows conservation of energy by trading potential and kinetic energy as it goes up and down. At the top of a hill the car is high and slow, so it has lots of potential energy and little kinetic energy; rushing down, the potential energy converts into kinetic energy, so it is fastest at the bottom. With a little energy lost to friction each time, every hill must be lower than the one before.

How does conservation of energy link to work?
ConceptualHowcomplexity 4

Work is the way energy is transferred by a force, and the work–energy theorem links the two: the net work done on an object equals its change in kinetic energy. Lifting a box does work against gravity and stores that energy as potential energy; letting it fall, gravity does work that turns the potential energy back into kinetic energy. Conservation of energy is really just careful book-keeping of all the work done and the energy stored.

Test yourself — a mixed set

Seven question formats, the way Beyond Dictionary serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000

Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.

Loading the question bank…
Question 1 of 16
Multiple choice

Key takeaways

  • Energy is never created or destroyed — it only changes form, so the total stays constant.
  • Kinetic energy is ½mv²; potential energy is mgh.
  • Mechanical energy (KE + PE) is conserved when there is no friction.
  • v = √(2gh) — the speed from a drop depends on the height, not the mass.
  • "Lost" energy becomes heat — which is why no machine is ever 100% efficient.

🪜 Where this lesson leads

Conservation of energy is one of the floors physics stands on. Master it and you have already started climbing toward:
Kinetic & potential energy
Work & power
Efficiency
Energy transformations
Momentum & collisions
Thermodynamics
Heat & entropy
Energy resources

Keep exploring

Energy never spends itself away — it only changes its disguise.

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