Use this as a quick reference for work as energy transfer, W = Fd cos θ, the sign of work, the work-energy theorem, and work as the area under an F versus displacement graph.
🧭 Plot Summary
Work is how a force changes the energy of a system: it is the amount of energy a force transfers into or out of a system as it acts over a distance. For a constant force, W = Fd cos θ, which means only the part of the force that points along the displacement counts. A force perpendicular to the motion, like the normal force on a sliding block or the tension on a ball swinging in a circle, changes the direction of the motion but does no work. Work is a scalar that can be positive (energy flows in), negative (energy flows out), or zero, and holding a heavy box still does no work at all, because nothing moves. The work-energy theorem ties it together: the net work on an object equals its change in kinetic energy. Gravity and springs are conservative, so their work depends only on the endpoints, while friction and air resistance are nonconservative, so their work depends on the path and the lost mechanical energy ends up as thermal energy and sound. When the force changes, the work is the area under the F versus displacement graph.
What you'll do in this lesson
- Describe work as the transfer of energy into or out of a system by a force exerted over a distance.
- Calculate the work done by a constant force at any angle with W = Fd cos θ.
- Decide when work is positive, negative, or zero, and recognize that perpendicular forces do no work.
- Apply the work-energy theorem to relate net work to a change in kinetic energy, including energy dissipated by friction.
- Find work as the area under an F versus displacement graph.
Why it matters
In Lesson 3.1 you learned what kinetic energy is. Work is the process that changes it, and the work-energy theorem is the bridge you'll cross again in Lesson 3.3 (potential energy), Lesson 3.4 (conservation of energy), and Lesson 3.5 (power, which is the rate of doing work). It also shows up on the AP exam as free-response reasoning about forces at angles and as graph-area problems.
✅ Self-Check Before You Roll On
Check off each item as you get there. These aren't grades — they're your own signal.