Everything you need at a glance — concepts, formulas, laws, units, real-world connections and "Did You Know" facts. Built for quick revision and deep understanding.
The building blocks of Work, Energy & Power — with real-life connections
Work is done when a force causes displacement in the direction of the force. Simply pushing a wall doesn't count — the wall must move!
A coolie carrying your luggage on his head (walking horizontally) does no work in physics — because the force (upward) is perpendicular to displacement (horizontal). Surprising, right?
For work to be done in physics, both must be true:
A satellite orbiting Earth experiences gravity but moves perpendicular to it — so gravity does zero work on the satellite!
Energy is the ability or capacity to do work. An object that can do work is said to possess energy. Energy and work are measured in the same unit — Joule.
When a fast cricket ball hits the stumps, it does work on them — this is its kinetic energy in action. The harder the ball hits, the more energy it carries!
Power is the rate of doing work. Two people may do the same amount of work — the one who does it faster is more powerful.
A 100W bulb and a 40W bulb can both light a room — but the 100W bulb does it faster (more energy per second). That's why it also costs more on your electricity bill!
The sign of work tells you the relationship between force and motion
Force and displacement are in the same direction (angle = 0°). The object speeds up.
Example: Pushing a box forward, apple falling from tree, engine accelerating a car
Force is opposite to displacement (angle = 180°). The object slows down.
Example: Friction on a sliding box, brakes on a car, gravity while throwing ball upward
Force and displacement are perpendicular (angle = 90°), or there is no displacement.
Example: Coolie carrying load horizontally, satellite in orbit, pushing a wall
Two faces of mechanical energy
Energy of motion. Any moving object has kinetic energy. The faster it moves, the more KE it has. KE increases with the square of speed.
If a car doubles its speed, its braking distance becomes 4 times longer — because KE is proportional to v². This is why speed limits save lives!
Energy stored due to position or configuration. A stretched rubber band, a raised weight, a compressed spring — all store potential energy.
When you pull back a catapult, you store elastic PE. When released, it converts to KE. Ancient armies used this to hurl boulders at castle walls!
The work done by the net force on an object equals the change in its kinetic energy:
Wnet = Kf − Ki = ΔKE
This means: if you do positive work on an object, its KE increases. If work done is negative, KE decreases (it slows down). The theorem bridges Newton's Second Law and energy — it's Newton's Second Law in scalar form.
The word "energy" comes from the Greek word energeia meaning "activity" or "operation." The physicist Thomas Young first used it in its modern scientific sense in 1807. Before that, scientists used "vis viva" (Latin for "living force") to describe what we now call kinetic energy!
Same topic, deeper treatment as you progress
Every formula — with all rearrangements, SI units and real-world context
A fielder runs 10 m to stop the ball, applying 5 N force in that direction: W = 5 × 10 = 50 J. But if the force is at 60° to direction of motion: W = 5 × 10 × cos60° = 5 × 10 × 0.5 = 25 J.
A 50g bullet at 200 m/s: KE = ½ × 0.05 × 40000 = 1000 J. A 2000 kg car at 25 m/s: KE = ½ × 2000 × 625 = 625,000 J. The car has 625× more KE — which is why car crashes are so devastating!
A 1 kg book on a 1 m high shelf has PE = 1 × 10 × 1 = 10 J. The PE is measured relative to your chosen zero level — on the ground, or on the floor below. The same object can have different PE values depending on where you set the zero!
Car shock absorbers use springs (k ≈ 15,000–25,000 N/m). When you hit a pothole (x = 5 cm = 0.05 m): V = ½ × 20000 × 0.0025 = 25 J. That's the energy the spring absorbs, keeping your ride smooth!
1 unit of electricity = 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. A 1500W geyser running 1 hour uses 1.5 units. At ₹8/unit, that's ₹12 per hour. Now you can calculate exactly why the electricity bill hurts!
The fundamental rules that govern work, energy and power
Before and after any transformation, the total energy stays the same. When a ball falls, gravitational PE converts to KE. When it hits the ground, that KE converts to heat, sound, and deformation — but nothing is lost. This law has never been violated in any experiment.
Koyna Dam stores water at height h. GPE = mgh. When water falls and spins turbines, GPE → KE → Electrical Energy. Maharashtra gets gigawatts of power this way — the same energy that was locked in raised water!
This law means a perpetual motion machine is impossible. Every machine that has ever been built eventually stops — it can't create energy from nothing. Thousands of patent applications for "free energy" machines are rejected by patent offices worldwide for this exact reason!
This is essentially Newton's Second Law in scalar form. It works for any force — constant or variable. It gives you a powerful shortcut: instead of calculating acceleration and time, just compare initial and final kinetic energies. The theorem holds in all inertial frames.
A car of mass 1500 kg moving at 60 km/h (≈16.7 m/s): KE = ½ × 1500 × 279 ≈ 209,000 J. Brakes must do negative work of exactly 209,000 J to stop it. That's the heat generated in your brake pads — which is why brakes get hot!
The negative sign means the spring force opposes the displacement (restoring force). The spring constant k (N/m) tells you how stiff the spring is. A stiffer spring has a higher k. The work done against spring force is stored as elastic PE = ½kx².
When a gymnast lands on a trampoline, the elastic bands stretch and store PE. That PE then launches the gymnast back up — converting all stored PE back to KE + GPE. The bouncing continues until energy is lost to heat and sound.
This follows from Newton's Third Law. The mutual forces between colliding objects are equal and opposite, so the net impulse is zero. Kinetic energy, however, may or may not be conserved depending on the type of collision.
| Property | Elastic Collision | Inelastic Collision |
|---|---|---|
| Linear Momentum | Conserved ✓ | Conserved ✓ |
| Kinetic Energy | Conserved ✓ | NOT conserved ✗ |
| Total Energy | Conserved ✓ | Conserved ✓ |
| Example | Billiard balls, atomic collisions | Car crash, clay balls sticking |
In a nuclear reactor, fast neutrons are slowed using a moderator (heavy water or graphite). When a neutron (mass m) collides elastically with deuterium (mass 2m), almost 90% of its kinetic energy is transferred in one collision. This is pure elastic collision physics!
Gravity and spring force are conservative. Work done by gravity in a closed path = 0. For such forces, we can define potential energy. Friction is non-conservative — it converts mechanical energy to heat, and the work done depends on the path length.
Energy exists in many forms — and can convert from one to another
Energy of motion. Moving car, flowing river, spinning wheel, blowing wind.
Energy due to height. Water in dam, book on shelf, elevated rollercoaster.
Stored in springs, rubber bands, bows. Released as kinetic energy.
Energy of random molecular motion. Friction converts KE to heat energy.
Stored in chemical bonds. Food, petrol, batteries release it when needed.
Energy of moving charges. Powers lights, motors, devices. Comes from generators.
Electromagnetic waves carry energy. Solar panels convert it to electrical energy.
Released from nuclear reactions. Powers stars and nuclear reactors.
Mechanical waves carrying energy through a medium. Tiny fraction of most processes.
Every gadget and activity is an energy transformation
Chemical (food) → Mechanical (muscles) → KE (motion) + PE (going uphill) + Heat (friction in bearings and tyres)
Chemical (battery) → Electrical (current) → Heat + Light (in bulb filament)
Gravitational PE (raised water) → KE (falling water) → KE (spinning turbine) → Electrical Energy
PE (at extreme) ⇌ KE (at bottom) — continuously. Gradually lost to heat and sound until it stops.
Light (solar) + Chemical (CO₂ + H₂O) → Chemical PE (glucose stored in plant)
KE (moving car) → Heat (brake pads, tyres) + Sound (screeching) — via friction (negative work)
PE is maximum at extremes, KE is maximum at the bottom. Their sum remains constant (ignoring air resistance).
The pendulum appears to violate conservation of energy because it slows down. But it doesn't! The energy is converted to heat and sound by air resistance and friction at the pivot. Total energy is still conserved — just spread out more.
Every measurement unit, constant, and important value at a glance
| Quantity | SI Unit | Symbol | Named After | Definition / Notes |
|---|---|---|---|---|
| Work Force × Displacement |
Joule | J | James Prescott Joule (1818–1889) | 1 J = 1 N × 1 m Work done when 1 N force displaces object by 1 m |
| Energy Capacity to do work |
Joule | J | Same as work | 1 kJ = 1000 J 1 calorie = 4.186 J; 1 kWh = 3.6 × 10⁶ J |
| Power Rate of doing work |
Watt | W | James Watt (1736–1819) | 1 W = 1 J/s 1 kW = 1000 W; 1 hp = 746 W |
| Force Push or pull |
Newton | N | Isaac Newton (1642–1727) | 1 N = 1 kg⋅m/s² F = ma |
| Mass Quantity of matter |
Kilogram | kg | — | SI base unit 1 kg = 1000 g |
| Displacement Shortest path, with direction |
Metre | m | — | SI base unit for length |
| Velocity / Speed Rate of displacement |
Metre per second | m/s | — | 1 km/h = 5/18 m/s ≈ 0.278 m/s Convert: km/h ÷ 3.6 = m/s |
| Spring Constant Stiffness of a spring |
Newton per metre | N/m | — | F = kx; higher k = stiffer spring |
| Electrical Energy What your bill measures |
Kilowatt-hour | kWh | — | 1 kWh = 3.6 × 10⁶ J Also called 1 "unit" on electricity bills |
9.8 m/s² (precise)
10 m/s² (for calculations)
Varies slightly: 9.78 at equator, 9.83 at poles
746 Watts
James Watt defined it to market his steam engines by comparing to horses. A typical horse actually sustains ~750 W.
1 grain of rice ≈ 4 J
Burning 1g of wood ≈ 17,000 J
1 litre of petrol ≈ 34 million J
Lightning bolt ≈ 1 billion J
LED bulb: 7–10 W
Ceiling fan: 70–80 W
Old incandescent: 60–100 W
Air conditioner: 1000–2000 W
Human body at rest: ~80 W
The unit Joule is named after James Prescott Joule (1818–1889), an English physicist who proved that heat is a form of energy. He measured the mechanical equivalent of heat to extraordinary precision — using a paddle wheel in water — and showed that 4.18 J of work produces exactly 1 calorie of heat. This was one of the key experiments establishing the Law of Conservation of Energy.
Speed: 1 km/h = 5/18 m/s | 36 km/h = 10 m/s | 72 km/h = 20 m/s
Energy: 1 kWh = 3.6 × 10⁶ J | 1 cal = 4.186 J | 1 eV = 1.6 × 10⁻¹⁹ J
Power: 1 hp = 746 W | 1 kW = 1000 W | 1 MW = 10⁶ W
Concepts made visual — for the moments when words aren't enough
As an object falls, PE decreases and KE increases — but their sum stays constant.
W = F × s (force in direction of displacement). The force F acts over displacement s, doing positive work.
KE = ½mv² — KE increases as the square of speed. Double the speed = 4× the KE!
At 60 km/h, a car has a certain KE. At 120 km/h (double), it has 4× the KE. The brakes must absorb 4× the energy — requiring 4× the stopping distance. This is the physics behind every speed limit on every road.
The spring force is linear (F = −kx), but PE is parabolic (V = ½kx²). At equilibrium, PE = 0 and KE is maximum.
Enter values and calculate — verify your answers instantly
W = F × s (Class 9) | W = F × d × cosθ (Class 11)
Ek = ½mv²
Ep = mgh
P = W/t | Also calculates electricity bill
How much does running an appliance cost per month?
Use the KE calculator: A cricket ball (0.16 kg) bowled at 140 km/h (38.9 m/s). KE = ½ × 0.16 × 38.9² ≈ 121 J. Now try the same ball at 160 km/h — notice how KE jumps by ~31% even though speed only increased by 14%? That's the v² effect!