Energy and Work

The universe’s currency — what it is, why it never disappears, and how to use it.

What energy actually is

Forget the textbook definition. Here’s the truth:

Energy is the ability to make something happen.

That’s it. If something can push, lift, heat, light, move, or break something else, it has energy. If it can’t, it doesn’t.

Energy is measured in joules (J). One joule is about the energy it takes to lift a small apple one meter into the air. Small unit. Everything else is just lots of joules.

The one rule that runs everything: conservation of energy

Energy is never created and never destroyed. It only changes form.

This is maybe the most important sentence in all of physics. Burn it in.

When you eat a sandwich, chemical energy from food turns into motion energy for your muscles, which turns into heat energy when you run. The total amount of energy never changes — it just keeps switching costumes.

Whenever you’re stuck on a physics problem, ask: “Where did the energy come from, and where did it go?” That single question solves problems that look impossible with forces alone.

The two main flavors of energy

Kinetic energy — the energy of motion

Anything that’s moving has kinetic energy. The formula:

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

Read it slowly: kinetic energy depends on mass and speed squared.

That squared is huge. It means:

• Double the speed → 4× the energy.
• Triple the speed → 9× the energy.

This is why a car crash at 100 km/h isn’t twice as bad as 50 km/h — it’s four times as bad. Speed is way more dangerous than people think. Engineers know this. Now you do too.

Potential energy — stored energy

Potential energy is energy that’s waiting to happen. A boulder on a cliff isn’t doing anything right now, but if it falls, it’ll do plenty. That “waiting” is potential energy.

The most common kind — gravitational potential energy — has a simple formula:

$PE = mgh$

• $m$ = mass
• $g$ = gravity (9.8 m/s² on Earth)
• $h$ = height above the ground (or whatever you call “zero”)

Higher up = more stored energy. Heavier = more stored energy. Same intuition you already have.

Other kinds of potential energy:

• Elastic — stretched spring, drawn bowstring
• Chemical — food, fuel, batteries
• Nuclear — atomic nuclei

All the same idea: energy stored, ready to be released.

Work — the bridge between force and energy

In physics, work has a very specific meaning:

Work is what happens when a force moves something.

$W = F \cdot d$

Force times distance. If you push a box with 10 N and it slides 2 m, you did 20 J of work on it.

The weird part

If you push against a wall as hard as you can for an hour and the wall doesn’t move — you did zero work on the wall. Physics doesn’t care that you’re tired. No motion = no work.

This isn’t physics being cruel. It’s physics being precise: work is specifically the energy transferred to an object by a force. No motion means no energy was transferred to the wall.

Watching energy transform: the roller coaster

This is the example that makes everything click.

1. At the top of the hill

   The coaster is barely moving. Lots of potential energy (high up), almost no kinetic energy (slow).

2. Halfway down

   It’s lower, so less PE. But it’s moving fast now, so more KE. The lost PE became KE. Total energy: same.

3. At the bottom

   Lowest point → minimum PE. Fastest point → maximum KE. PE got fully converted into KE.

4. Climbing the next hill

   KE turns back into PE as it slows down going up. The trade reverses.

In a perfect, frictionless world, the coaster would keep going forever, trading PE and KE. In the real world, friction and air resistance slowly bleed energy off as heat. Energy isn’t “lost” — it just left the coaster and warmed up the rails and the air a tiny bit.

This is why understanding energy is so powerful: you don’t have to track every force at every moment. You just compare the start and the end. “Started with X joules of PE, ended with X joules of KE.” Done.

Power — how fast energy is used

Energy is how much. Power is how fast.

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

Measured in watts (W). One watt = one joule per second.

• A 60 W lightbulb uses 60 joules every second.
• A 1500 W microwave uses 1500 joules every second.
• A human running uses around 700 W.
• A car engine puts out about 100,000 W (≈ 134 horsepower).

Same energy, faster delivery = more power. Two people can lift the same box up the same stairs, but the one who runs uses more power, not more energy.

The mechanical engineer’s secret

Whenever you can choose between solving a problem with forces ($F = ma$) or energy (conservation), try energy first. It’s almost always shorter.

Why? Because energy doesn’t care about the path. A ball that falls 10 m gains the same KE whether it fell straight down, slid down a ramp, or took a loopy roller-coaster track. Forces would force you to track every wiggle. Energy just asks: how high did you start, how high did you end?

Next: Momentum

The other thing that’s always conserved — and the secret to understanding collisions.