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.
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:
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:
Searched as: law of conservation of energy, kinetic and potential energy, energy transformations, ½mv², mgh, efficiency.
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
Set a drop height and mass to see what they mean.
In plain terms: energy comes in forms — motion (kinetic) and stored (potential) among them — and as they swap, the total stays the same.
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.
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.
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
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.
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.
A few ideas about energy are so common they feel obvious. Tap a card to flip it and bust the myth.
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.
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.
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.
Once we could track energy through every change of form, we learned to store it, move it, and turn one kind into another at will.
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.
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.
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.
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.
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.
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.
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.
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.
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.
| Feature | Kinetic energy | Potential energy |
|---|---|---|
| What it is | Energy of motion | Stored energy of position or state |
| Formula | KE = ½mv² | Gravitational PE = mgh |
| Depends on | Mass and speed² | Mass, gravity and height |
| Example | A speeding car | A raised hammer |
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.
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.
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.
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.
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.
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.
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.
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.
Energy never spends itself away — it only changes its disguise.