# Work, Energy, and Power

> AP Physics C: Mechanics · AP Physics C Mechanics
> Source: https://www.owlsprep.com/study/ap-physics-c-mech-u3-overview/
> Weight: 14-18% of overall AP exam score

This unit introduces core concepts of work, energy, and power—powerful problem-solving tools that simplify analysis of motion for complex systems with non-constant forces.

**Prerequisites:** [Unit 2: Newton's Laws of Motion](https://www.owlsprep.com/study/ap-physics-c-mech-u2-overview/)

## Learning objectives

- Calculate work done by both constant and variable forces acting on a system
- Apply the work-energy theorem to relate net work to changes in an object's kinetic energy
- Relate conservative force functions to potential energy curves and identify equilibrium positions
- Use conservation of mechanical energy to analyze motion in systems with conservative and non-conservative forces
- Calculate average and instantaneous power for work done by forces in mechanical systems

## 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](https://www.owlsprep.com/study/ap-physics-c-mech-u3-conservation-of-energy/) — Learn how energy is conserved in closed systems, and solve for motion of systems with internal energy changes.
- [AP Physics C: Mechanics Forces and potential energy](https://www.owlsprep.com/study/ap-physics-c-mech-u3-forces-and-potential-energy/) — Derive the relationship between conservative force functions and potential energy, and identify equilibrium from energy graphs.
- [AP Physics C: Mechanics Power](https://www.owlsprep.com/study/ap-physics-c-mech-u3-power/) — Define instantaneous and average power, and calculate power transfer for work done by forces in moving systems.
- [AP Physics C: Mechanics Work and the work-energy theorem](https://www.owlsprep.com/study/ap-physics-c-mech-u3-work-and-the-work-energy/) — Introduce work for constant and variable forces, and derive the theorem that relates net work to change in kinetic energy.

## Common pitfalls

- **Wrong:** Treating all forces as conservative when applying conservation of energy.
  - Why it fails: Non-conservative forces like friction change the total mechanical energy of a system.
  - Correct: Add the work done by non-conservative forces to your total energy balance for the system.
- **Wrong:** Using the wrong sign in the force-potential energy relationship.
  - Why it fails: A sign error leads to incorrect direction of the conservative force.
  - Correct: Remember the relationship $F_x = -\frac{dU}{dx}$ — force is the negative derivative of potential energy.

## Cheatsheet

| Concept | Formula |
| --- | --- |
| Work (variable force) | $W = \int_{x_1}^{x_2} F_x dx$ |
| Work-Energy Theorem | $W_{net} = \Delta K = K_f - K_i$ |
| Conservation of Mechanical Energy | $K_i + U_i + W_{nc} = K_f + U_f$ |
| Force from Potential Energy | $F_x = -\frac{dU}{dx}$ |
| Average Power | $P_{avg} = \frac{\Delta W}{\Delta t} = F v_{avg}$ |
| Instantaneous Power | $P = \vec{F} \cdot \vec{v}$ |
| 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.

- [AP Physics C: Mechanics Conservation of energy](https://www.owlsprep.com/study/ap-physics-c-mech-u3-conservation-of-energy/)
- [AP Physics C: Mechanics Center of Mass](https://www.owlsprep.com/study/ap-physics-c-mech-u4-center-of-mass/)
- [Work and the Work-Energy Theorem](https://www.owlsprep.com/study/ap-physics-c-mech-u3-work-and-the-work-energy/)

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