Unit Overview

Work, Energy, and Power

AP Physics C: Mechanics· 5 min read 📊 14-18% of overall AP exam score

1. Unit at a Glance

Energy-based approaches to mechanics often let you solve problems much faster than direct application of Newton's laws, especially when working with variable forces or unknown intermediate motion. This unit progresses from core definitions to foundational principles, connecting work to kinetic energy, potential energy to conservative forces, and ending with the concept of power as a rate of energy transfer.

Below are the sub-topics you will explore in this unit:

AP Physics C: Mechanics Conservation of energy

Learn how energy is conserved in closed systems, and solve for motion of systems with internal energy changes.

★★★⏱ 10 min

AP Physics C: Mechanics Forces and potential energy

Derive the relationship between conservative force functions and potential energy, and identify equilibrium from energy graphs.

★★★★⏱ 12 min

AP Physics C: Mechanics Power

Define instantaneous and average power, and calculate power transfer for work done by forces in moving systems.

★★⏱ 5 min

AP Physics C: Mechanics Work and the work-energy theorem

Introduce work for constant and variable forces, and derive the theorem that relates net work to change in kinetic energy.

★★★⏱ 8 min

2. Common Pitfalls

Wrong move:

Treating all forces as conservative when applying conservation of energy.

Why:

Non-conservative forces like friction change the total mechanical energy of a system.

Correct move:

Add the work done by non-conservative forces to your total energy balance for the system.

Wrong move:

Using the wrong sign in the force-potential energy relationship.

Why:

A sign error leads to incorrect direction of the conservative force.

Correct move:

Remember the relationship $F_{x} = - \frac{d U}{d x}$ — force is the negative derivative of potential energy.

3. Quick Reference Cheatsheet

Concept	Formula
Work (variable force)	$W = \int_{x_{1}}^{x_{2}} F_{x} d x$
Work-Energy Theorem	$W_{n e t} = Δ K = K_{f} - K_{i}$
Conservation of Mechanical Energy	$K_{i} + U_{i} + W_{n c} = K_{f} + U_{f}$
Force from Potential Energy	$F_{x} = - \frac{d U}{d x}$
Average Power	$P_{a v g} = \frac{Δ W}{Δ t} = F v_{a v g}$
Instantaneous Power	$P = F \cdot v$
Total Mechanical Energy	$E = K + U$

What's Next

Begin your study of this unit by navigating to the first sub-topic below. Once you complete all sub-topics in Work, Energy, and Power, move on to the first sub-topic of the next unit on systems of particles and linear momentum. All sub-topics include targeted practice and detailed explanations aligned to AP exam expectations.