In everyday English, "work" can mean almost anything — studying, sitting in a meeting, even just feeling tired. In physics it means something very specific:

Work is the amount of energy transferred when an external force causes an object to move over a certain distance.

Here's the key insight that trips people up: if there's no movement, no work is done — no matter how hard you push. Imagine leaning your whole body weight against a brick wall for ten minutes. You'll be exhausted, sweating, and your muscles will genuinely be using energy — but in the physics sense, zero work is done on the wall, because the wall didn't move anywhere. Work only "counts" once there's displacement.

If the force pushes in the direction the object is already moving, the object gains energy. If the force pushes against the motion (like friction), the object loses energy — work is being done against it, converting its kinetic energy into other forms like heat and sound.

Most of the time in real life, forces aren't perfectly parallel to the direction of travel. Think about pulling a sledge with a rope over your shoulder — the rope pulls up and forward, but the sledge only moves forward along the ground.

In these cases, you can't use the whole force — only the component of the force that's actually pointing in the direction of motion does any useful work. The rest of the force (the part pointing "sideways" to the motion) does no work at all, because there's no displacement in that direction.

Kinetic energy (E_k) is the energy an object possesses purely because it's moving. A parked car has zero kinetic energy; the same car doing 100 km/h has a lot. The faster something moves, the more kinetic energy it carries.

Where does this formula come from? It's not just handed down from nowhere — it comes directly from the work-energy relationship you just learned. If a constant force F accelerates a mass m from rest over a distance d, the work done on it is W = Fd. Using F = ma (Newton's Second Law) and the suvat equation v² = u² + 2as (with u = 0, s = d), you can substitute through and show that the work done equals exactly ½mv². Since all of that work has gone into speeding the object up, that ½mv² is now "stored" in the object as kinetic energy — that's the derivation.

Gravitational potential energy (E_p or GPE) is energy stored in an object because of its position within a gravitational field — essentially, how high up it is. Lift something up and you're doing work against gravity; that work gets "banked" as GPE, ready to be released (usually converted into kinetic energy) the moment the object falls.

This equation is only valid for a uniform gravitational field — i.e. situations reasonably close to the Earth's surface, where g doesn't meaningfully change with height. (You'll meet a different, more general GPE formula for large-scale orbital situations elsewhere in the course.) By convention, ground level is usually taken as the "zero" of potential energy, and everything is measured as a change relative to that.

Just like with kinetic energy, this formula is derived from the work-done concept: lifting a mass m through height h requires overcoming its weight (mg) over that distance, so the work done is W = F × d = mg × Δh — and since all that work has gone into raising the object, that same amount is now stored as GPE.

This is one of the most fundamental laws in all of physics: in a closed system, the total energy in is always equal to the total energy out. Energy doesn't vanish and it doesn't appear from nowhere — it just changes form, or moves from one place to another.

In this chapter, that principle is most often applied to swapping between kinetic energy and gravitational potential energy. Classic examples:

• A pendulum swinging — GPE at the top of each swing converts fully to KE at the bottom, and back again.
• An object in free fall — GPE lost equals KE gained (ignoring air resistance).
• Skiing or skydiving — gravity does the work of speeding you up as your height (and GPE) decreases.

In an "ideal" calculation, we usually assume all the GPE lost converts to KE gained — but in reality, some energy always leaks away as heat (from friction/air resistance) or sound. Exam questions will often tell you what percentage is "lost" so you can factor that into a more realistic calculation.

Power is the rate at which energy is transferred (or equivalently, the rate at which work is done). It doesn't tell you how much total energy was transferred — it tells you how quickly that transfer happened.

Two engines could do exactly the same amount of work (say, lifting an identical crate to the same height) — but if one does it in 2 seconds and the other takes 20 seconds, the first engine is ten times more powerful, even though the total work done is identical.

Efficiency measures how well a system converts the energy you put in into the energy you actually want out. No real machine is 100% efficient — some energy always escapes as heat, sound, or other "wasted" forms.

What counts as "useful" versus "wasted" depends entirely on the system: in a lightbulb, light is useful and heat is wasted; in a heater, heat is useful and any sound produced is wasted. It's the same physics, just a different goal.