Kinetic Energy

Kinetic energy is the energy an object has because it is moving. The faster an object moves and the more massive it is, the more kinetic energy it carries. A flying tennis ball has kinetic energy. A falling raindrop has it. A speeding car has it. A walking person has it. Even tiny molecules of gas in the air have kinetic energy (which is what we feel as temperature). Kinetic energy is one of the most common forms of energy in everyday life, and many machines exist purely to convert other energy forms into useful kinetic energy.

  • What it isEnergy of motionCarried by any moving object
  • FormulaKE = 1/2 m v^2Half mass times speed squared
  • Double the speed4 times the energyQuadratic dependence
  • Double the mass2 times the energyLinear dependence
  • ExamplesMoving cars, falling rain, wind, running peopleEverywhere
  • Stops byConverting to other formsHeat, sound, deformation

How to calculate kinetic energy

The formula for kinetic energy is:

KE = 1/2 x m x v^2

Where:

  • KE is kinetic energy in joules.
  • m is mass in kilograms.
  • v is speed in metres per second.

Two interesting things to notice:

  • Doubling the mass doubles the kinetic energy (linear). A 2 kg ball at 5 m/s has twice the energy of a 1 kg ball at the same speed.
  • Doubling the SPEED quadruples the kinetic energy (squared). A car going 60 km/h has 4 times the kinetic energy of one going 30 km/h. A car at 90 km/h has 9 times.

Some examples

  • A 0.05 kg tennis ball at 30 m/s: 22.5 J.
  • A 0.05 kg tennis ball at 60 m/s: 90 J (4 times more).
  • A 70 kg person walking at 1.5 m/s: 79 J.
  • A 70 kg person running at 5 m/s: 875 J.
  • A 1,500 kg car at 30 m/s (108 km/h): 675,000 J.
  • A 250 tonne airliner at 250 m/s (900 km/h): 7.8 billion joules.
  • An astronaut on the ISS at 7,700 m/s: 70 kg x 7700^2 / 2 = 2.1 billion joules.
Fact The reason fast cars are so dangerous is the squared dependence on speed. A car at 90 km/h has 9 times the kinetic energy of the same car at 30 km/h. In a crash, all that energy has to go somewhere: typically into bending metal, breaking glass and (very dangerously) injuring people. That is why speed limits are vital and braking distances grow rapidly with speed.

Where you see kinetic energy

  • Moving vehicles: every car, train, plane, bike, ship and rocket has kinetic energy.
  • Wind: moving air. Wind turbines convert it to electricity.
  • Water: flowing rivers and waves. Hydroelectric and tidal power stations capture it.
  • People and animals: anything moving.
  • Falling objects: a falling raindrop, a leaf, an apple.
  • Spinning things: a wheel, a fan, a frisbee. (Rotational kinetic energy is a special case.)
  • Molecules in air: even still air contains molecules buzzing about at high speed. Their average kinetic energy is what we feel as temperature.

How kinetic energy is gained or lost

An object gains kinetic energy when a force speeds it up:

  • A football gains kinetic energy when you kick it.
  • A car gains kinetic energy as its engine accelerates it.
  • A falling apple gains kinetic energy as gravity speeds it up.

An object loses kinetic energy when a force slows it down. The lost kinetic energy turns into other forms:

  • A car braking loses kinetic energy as heat in the brake pads.
  • A bouncing ball loses kinetic energy with each bounce, mostly as heat and sound in the rubber and floor.
  • Wind hitting a turbine loses kinetic energy as electrical energy is produced.
Did you know? Modern electric and hybrid cars use a clever trick called regenerative braking. Instead of just turning kinetic energy into wasted heat in the brake pads, the motor runs in reverse and acts as a generator, capturing the cars kinetic energy and putting it back into the battery. This makes electric cars about 20 to 30 per cent more efficient in city driving, where lots of energy would otherwise be wasted slowing down.

Temperature is kinetic energy

One surprising fact: temperature is really a measure of the average kinetic energy of the particles in a material. Hot things have fast-moving particles. Cold things have slow-moving particles. Absolute zero (-273.15 C) would be the temperature at which all particle motion essentially stops.

That is why heat and motion are so closely connected. Rub your hands together and they warm up (friction converts kinetic energy into heat). Hammering a nail repeatedly heats the nail (kinetic energy of the hammer becomes heat in the nail).

Kinetic energy in sport

Nearly every sport is partly a competition in managing kinetic energy:

  • Football: getting a fast ball into goal or away from danger.
  • Tennis: a high-energy serve is hard to return.
  • Cricket: fast bowlers deliver balls with great kinetic energy.
  • Rugby: a heavy player at speed has enormous kinetic energy.
  • Boxing: a fast punch delivers more kinetic energy.
  • Athletics: sprinters convert chemical energy in food into kinetic energy as they run.
Try this Roll a ball gently down a slope and measure how far it travels along the flat floor at the bottom. Then roll the same ball from twice the height. It rolls much further because it has 4 times the kinetic energy at the bottom (twice the speed squared). Try the same with a heavier ball: it travels even further because it had more starting potential energy.
Deeper dive: how kinetic energy lights cities through hydroelectric power

One of the cleanest and oldest ways of generating electricity is by capturing the kinetic energy of flowing water. Hydroelectric power currently provides about 16 per cent of the worlds electricity, and over 60 per cent in some countries like Norway, Brazil and Canada.

The principle is simple. A river is dammed to create a reservoir. Water from the reservoir flows down through pipes to a turbine far below. As the falling water hits the turbine blades, it transfers its kinetic energy. The turbine spins a generator, producing electricity that flows out through wires to homes and factories.

The energy chain looks like this:

  1. Solar energy evaporates water from oceans and lakes (heat from the Sun).
  2. Potential energy: clouds carry the vapour to higher altitudes. Rain falls in the mountains.
  3. Potential energy: water sits in the reservoir, held up by the dam.
  4. Kinetic energy: water flows down through pipes, accelerating under gravity.
  5. Mechanical energy: water turns the turbine blades.
  6. Electrical energy: the generator produces voltage and current.

Hydroelectric power is renewable, very low-carbon (once the dam is built) and can supply power on demand (you can hold back water when not needed and release it when extra electricity is required). The biggest hydroelectric plant in the world is the Three Gorges Dam on the Yangtze River in China, with a capacity of 22.5 gigawatts (about the same as 20 large nuclear power stations).

The trade-offs are real. Big dams flood huge areas (the Three Gorges Dam displaced 1.3 million people). They can disrupt fish migrations and river ecosystems. But for low-carbon, reliable, on-demand electricity, hydroelectric power remains one of the best technologies humanity has, all powered by the same falling-water kinetic energy a mill wheel uses.

For more, see potential energy and conservation of energy.