Work, Energy & Power

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Work, Energy & Power

The Big Idea Whenever a force moves something, energy gets transferred from one place (or one form) to another — and no matter how it moves around, the total amount of energy never changes.

Summary — What This Chapter Covers

Work is done whenever a force causes something to move through a distance — it's how energy actually gets "delivered" from a force to an object.
If the force isn't perfectly aligned with the motion, you only count the part of the force that is aligned with the motion (that's where the cos θ / sin θ comes from).
Kinetic energy is the energy something has purely because it's moving — the faster it goes, the more it has, and it goes up with the square of speed, not speed itself.
Gravitational potential energy is "stored height" — energy an object has because it's been lifted up against gravity.
The Principle of Conservation of Energy says energy is never created or destroyed — only transferred between forms (like GPE ↔ KE) or converted to less useful forms (like heat or sound).
Power is simply how fast energy is being transferred — the same amount of work done quickly means high power; done slowly means low power.
Efficiency measures how much of the energy you put into a system actually comes out as something useful, versus how much is "wasted" (usually as heat).

1. Work

What is "work" in physics?

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.

Think of it like this Work is like a "delivery receipt" for energy. A force can want to give energy to an object all day long, but the receipt only gets signed — the transfer only actually happens — once the object has moved. No movement, no delivery, no work done.

Key Formula — Force Parallel to Motion

ΔW = F Δs

ΔW = work done, in joules (J)
F = force applied, in the same direction as the motion (N)
Δs = distance moved (m)

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.

When the force is at an angle

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.

component of the force that's actually pointing in the direction of motion

Key Formula — Force at an Angle θ

W = Fs cos θ or W = Fs sin θ

Use cos θ when θ is measured from the horizontal (the direction of motion)
sin θ vertical

5. Power

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