Energy, Work and Power

Modern science doesn't talk about "types of energy" so much as stores:

• Kinetic — energy of moving objects.
• Gravitational potential — raised mass in a gravitational field.
• Elastic potential — stretched or compressed springs and bands.
• Thermal (internal) — total kinetic + potential energy of particles in a substance.
• Chemical — stored in chemical bonds (food, fuels, batteries).
• Nuclear — stored in atomic nuclei (released in fission/fusion).
• Magnetic and electrostatic — stored in fields between magnets or charges.

Energy moves between stores by four transfer pathways:

1. Mechanically — by a force moving through a distance (pushing, pulling, lifting).
2. Electrically — by a current flowing.
3. By heating — when there is a temperature difference.
4. By radiation — light, infrared, microwaves, sound.

A cyclist pedalling uphill transfers energy chemically (food) → kinetic (legs and bike) → gravitational potential (raised mass). Some is also transferred to thermal (warmth in muscles and tyres).

Conservation of energy: in a closed system, the total energy never changes. It only moves from one store to another. There is no "lost" energy — only wasted energy that ends up in a less useful store (usually thermal, dissipated to surroundings).

When a force moves something through a distance, energy is transferred. The amount transferred is the work done:

$W = F \, d$

with W in joules (J), F in newtons (N), d in metres (m).

Worked example. A child pushes a 200 N box 5 m across a floor. Work done = 200 × 5 = 1 000 J.

If the force is at an angle to the direction of motion, only the component along the motion counts. A force applied perpendicular to motion (like normal contact from the floor on a moving box) does no work — the box doesn't move in that direction.

Kinetic energy (energy of motion):

$\text{KE} = \tfrac{1}{2} m v^2$

A 1 500 kg car at 14 m/s has KE = ½ × 1 500 × 14² = 147 000 J = 147 kJ.

Note that doubling the velocity quadruples the kinetic energy — which is why high-speed crashes are so much more destructive than slow ones.

Gravitational potential energy (energy of position in a gravitational field):

$\text{GPE} = m \, g \, h$

A 60 kg climber 30 m up a wall has GPE = 60 × 9.8 × 30 = 17 640 J.

Energy conversion problem. A 500 g ball is dropped from 1.8 m. Find its speed just before it hits the ground (ignore air resistance).

GPE at start = mgh = 0.5 × 9.8 × 1.8 = 8.82 J. At the bottom, all GPE has become KE: ½mv² = 8.82 J. → v² = 2 × 8.82 / 0.5 = 35.28 → v ≈ 5.94 m/s.

Power is the rate at which energy is transferred:

$P = \frac{E}{t}$

Units: watts (W). 1 watt = 1 joule per second.

A 60 W lamp transfers 60 J of electrical energy every second. A 100 W treadmill burns ~100 J of chemical energy per second.

Efficiency is the fraction of input energy that is useful:

$\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}}\times 100\%$

A car engine might be only 25% efficient — the other 75% becomes thermal energy in the engine, exhaust and tyres. An LED lamp is around 90% efficient (most goes to light); an incandescent bulb only 5% (most goes to heat).

The thicker the arrow on a Sankey diagram, the more energy is going that way.