#AP Physics C: Mechanics - Energy Review 🚀

Hey! Let's get you prepped for the exam with a super-focused review of energy. We'll break it down, make it stick, and get you feeling confident. Let's do this!

#Conservation of Energy: The Big Picture

#The Core Idea

At its heart, the Law of Conservation of Energy states that:

In a closed system, the total energy remains constant. Energy can transform from one form to another, but it cannot be created or destroyed.

Think of it like this: you have a fixed amount of money, you can exchange it for different currencies, but the total amount remains the same. 💡

• Key Concept: Energy is a conserved quantity. It's all about transfers and transformations, not creation or destruction.
• Forms of Energy: Kinetic (motion), potential (position), thermal (heat), chemical, nuclear, etc. All are part of the total energy.

#Mathematical Representation

The total mechanical energy (ME) of a system is the sum of its kinetic energy (K) and potential energy (U):

$$ME = K + U$$

• Kinetic Energy (K): Energy of motion. $K = \frac{1}{2}mv^2$
• Potential Energy (U): Stored energy due to position or configuration. Examples include gravitational potential energy ($U_g = mgh$) and spring potential energy ($U_s = \frac{1}{2}kx^2$).

#Work and Nonconservative Forces

When nonconservative forces (like friction or air resistance) do work on a system, the total mechanical energy changes. The work done by these forces is:

$$\Delta ME = W_{nonconservative}$$

• Important Note: This work can either add or remove energy from the system.
• Conservative vs. Nonconservative: Conservative forces (gravity, spring) conserve total mechanical energy; nonconservative forces do not.

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In a conservative system (where only c...