AP Physics C: Mechanics
Advanced Placement Physics C: Mechanics with calculus-based physics principles.
Work, Energy, and Power
The Language of Energy
Work, energy, and power connect forces with the ability to cause movement.
Work
Work is done when a force moves an object: \( W = \int \vec{F} \cdot d\vec{r} \). With calculus, we handle varying forces and curved paths.
Kinetic and Potential Energy
- Kinetic Energy (\(KE\)): Energy of motion, \( KE = \frac{1}{2}mv^2 \).
- Potential Energy (\(PE\)): Stored energy due to position, like \( PE = mgh \) for gravity.
Conservation of Energy
Energy can't be created or destroyed, only transformed. Calculus helps analyze systems where energy changes form.
Power
Power is the rate at which work is done: \( P = \frac{dW}{dt} \).
Applications
Engines, roller coasters, and even jumping frogs all rely on the interplay of work, energy, and power.
Key Formula
\[W = \int \vec{F}\cdot d\vec{r}\]
Examples
A crane lifting a load uses energy, does work, and requires power.
A sprinter's muscles convert chemical potential energy into kinetic energy.
In a Nutshell
Work, energy, and power describe how forces transfer and transform energy to make things happen.