Principle of Conservation of Energy

Energy is the thing that never goes missing. Push a swing, switch on a kettle, drop a ball — whatever happens, the energy you started with is all still there afterwards. It might have moved somewhere else or changed into a different form, but the total never budges. That single idea — the principle of conservation of energy — is one of the most powerful tools in physics, because it lets you follow energy from start to finish without worrying about every detail in between.

What conservation of energy actually says

The principle of conservation of energy can be stated in one line:

So the total amount of energy always stays the same. What changes is how that energy is shared out between the different forms. When nothing is happening — a system in equilibrium — the energy just sits there. The moment something changes, energy gets transferred, and that transfer is what makes things happen.

The forms energy comes in

Energy is a single quantity, but it shows up wearing different costumes. Here are the ones you’ll meet most:

• Kinetic — the energy of anything that’s moving.
• Gravitational potential — energy something gains when it’s lifted up, and loses when it falls.
• Elastic potential — energy stored in a stretched or squashed spring (sometimes called strain energy).
• Chemical — energy locked inside a chemical substance, like fuel or a battery.
• Nuclear — energy held within the nucleus of an atom.
• Internal (thermal) — energy something has because of its temperature.

The first three — kinetic, gravitational potential and elastic potential — are grouped together as mechanical energy, because they’re the ones that swap back and forth in moving mechanical systems like springs, pendulums and falling objects.

Energy transfers and dissipation

Every time energy is transferred from one form to another, some of it leaks away into the surroundings — nearly always as thermal energy that spreads out and can’t easily be used again. We say that energy has been dissipated, and because it’s no longer useful, we call it wasted energy.

Take a kettle. It turns electrical energy into thermal energy in the heating element, and most of that usefully heats the water. But some warms the plastic casing, and some drifts off into the surrounding air. The transfer that heats the water is the useful one; the rest is wasted. Which is which always depends on what you actually want the system to do.

Because energy is conserved, the useful and wasted parts must add up to everything you put in:

Where the energy goes: useful vs wasted

In a mechanical system, the energy that gets transferred is the same as the work done — the two are just different names for the same thing. Some everyday examples of energy flowing between forms:

• A falling object in a vacuum transfers gravitational potential energy into kinetic energy.
• A mass on a horizontal spring swaps elastic potential energy for kinetic energy.
• A battery turns chemical energy into electrical energy.
• A car engine turns chemical energy from fuel into kinetic energy of the car.
• A person on a trampoline cycles between elastic potential, kinetic and gravitational potential energy.

Often there’s also work done against resistive forces like friction. That work doesn’t vanish — it shows up as thermal energy. So when something slides up a rough slope, for instance, the books still balance:

Conservation of mechanical energy

Here’s the trick that makes this idea so useful. If we can ignore friction and drag, then no mechanical energy leaks away as heat, so the mechanical energy alone is conserved. That means whatever one form loses, another form gains — exactly. For a falling object or a swinging pendulum: