Potential Energy

Potential energy is energy that is stored up, ready to be released. A book sitting on a high shelf has potential energy because gravity could pull it down if it fell. A stretched rubber band has potential energy because it could snap back if released. A piece of food has potential energy in its chemical bonds. Anything with stored energy that could be released has potential energy. The word "potential" means "could happen": the energy is just waiting for the right conditions to turn into other forms.

  • What it isStored energyCould be released later
  • Gravitational PEGPE = m x g x hMass x gravity x height
  • Elastic PEStretched or squashed springsRubber bands, drawn bows
  • Chemical PEIn bonds between atomsFood, fuel, batteries
  • Nuclear PEInside atomic nucleiReleased in fission and fusion
  • Switching to kineticWhen force is releasedDrop the book, release the spring

Gravitational potential energy

The most common type of potential energy is gravitational potential energy (GPE): the energy an object has because of its height above the ground. The formula is:

GPE = m x g x h

Where m is the mass in kg, g is gravitational acceleration (9.8 m/s2 on Earth), and h is the height in metres. The higher you lift something and the heavier it is, the more energy is stored.

Examples:

  • A 1 kg ball lifted 1 metre above the ground has 9.8 J of GPE.
  • A 70 kg person at the top of a 10-storey building (about 30 m) has 20,580 J.
  • A 10,000 kg helicopter at 1,000 m altitude has 98 million joules.

Drop the object and gravity converts the GPE into kinetic energy: the higher the drop, the faster the impact.

Elastic potential energy

Elastic potential energy is stored in stretched, compressed or bent objects. The classic example is a spring: squash it and energy is stored in the squashed coils. Release it and the spring snaps back, releasing the stored energy as motion.

Other examples:

  • A stretched rubber band.
  • A drawn bow (storing energy to launch an arrow).
  • A wind-up toy with a coiled spring.
  • A compressed pogo stick.
  • A trampoline as someone lands on it.
  • A jumping spider (which stores energy in special internal springs before jumping).
Fact A modern bow used by an Olympic archer can store about 30 to 50 joules of elastic potential energy at full draw. When released, almost all that energy goes into the arrow, which can fly at 80 m/s (290 km/h) or more. That is enough to bury an arrow tip 10 cm deep into a wooden block. The bows ancient predecessors, made from a single piece of yew wood, work on exactly the same principle.

Chemical potential energy

Chemical potential energy is stored in the bonds between atoms in molecules. Different molecules store different amounts of energy in their bonds. When the bonds rearrange in a chemical reaction (like burning fuel or digesting food), some of the stored energy is released, usually as heat and light.

Examples of chemical energy storage:

  • Food: glucose, fats and proteins. Your body releases this slowly with enzymes for muscle and brain power.
  • Fuels: petrol, diesel, gas, coal, wood. Burning releases the energy as heat.
  • Batteries: chemicals inside release electrical energy when the circuit is connected.
  • Explosives: release huge amounts of chemical energy very quickly.

See chemical energy for more.

Nuclear potential energy

Inside every atomic nucleus, enormous amounts of energy are stored as nuclear potential energy. The protons and neutrons in the nucleus are bound together by the strong nuclear force, and breaking apart or joining together releases or absorbs a tremendous amount of energy.

  • Nuclear fission: splitting heavy nuclei (like uranium-235) releases energy. Used in nuclear power stations and atomic bombs.
  • Nuclear fusion: combining light nuclei (like hydrogen) into heavier ones releases even more energy. This is what powers the Sun and all stars.
Did you know? A single gram of uranium-235, fully used in a nuclear reactor, can produce about 24,000 kilowatt-hours of electricity: enough to power an average UK home for over 6 years. The same amount of energy would require burning about 2,500 kg of coal. Nuclear fuels store huge amounts of energy in tiny volumes, which is why nuclear plants only need refuelling once every year or two.

Potential becoming kinetic

The most famous demonstration of potential energy is a pendulum:

  • At the highest point of its swing, the pendulum is momentarily still: maximum potential energy, zero kinetic energy.
  • As it swings downward, potential energy converts into kinetic energy. Lowest point of the swing has maximum kinetic energy, lowest potential energy.
  • It then swings up the other side, converting kinetic back into potential energy.
  • If there were no friction, this cycle would repeat forever. In reality, each swing is slightly smaller as some energy is lost to air friction and heat.

This swap between potential and kinetic energy is one of the most common patterns in physics. It governs pendulum clocks, rollercoasters, planet orbits and even oscillating molecules.

Try this Pull back a swing on a playground and let it go from a height. As it swings down, potential energy turns into kinetic energy. At the bottom, you are going fastest. Going up the other side, kinetic turns back into potential. Each successive swing is slightly smaller because air friction has bled away a little energy. The same conversion is happening every time you go up and down on a swing or down a slide.
Deeper dive: how a pumped storage hydroelectric station stores energy for the grid

One of the trickiest problems in modern electricity supply is matching how much is generated to how much is being used. Demand changes throughout the day: peaks at breakfast, evening dinner time and during big TV events. Renewable supply (wind and solar) varies too.

A clever solution is the pumped storage hydroelectric station. This is a hydroelectric plant with two reservoirs: one high up, one low down. When electricity is cheap and plentiful (windy nights, sunny midday), the station uses the surplus energy to pump water from the lower reservoir up to the higher one. The water now has lots of gravitational potential energy.

When electricity is in high demand (during the evening or a cold snap), water is allowed to flow back down through turbines, generating electricity for the grid. The potential energy stored in the high reservoir becomes the electrical energy people need.

Pumped storage is one of the most efficient ways to store energy on a grid scale: about 70 to 80 per cent of the energy used to pump water uphill comes back as electricity when needed. The largest UK example is the Dinorwig Power Station in Wales, hidden inside a mountain. It can switch from zero to its full 1.7 gigawatts of output in just 16 seconds, balancing the grid during sudden demand peaks (like the famous "tea-time spike" when half of Britain switches on the kettle after a popular TV programme).

As more renewable energy is added to grids worldwide, pumped storage and similar technologies (battery storage, compressed air, hydrogen) are becoming ever more important. They all rely, in different ways, on the same simple physics idea: store energy by lifting things up, releasing the stored potential energy when its needed.

For more, see kinetic energy and chemical energy.