#AP Physics C: Mechanics - Energy & Potential Review 🚀

Hey there, future physicist! Let's get you prepped for the exam with a high-impact review of energy and potential. We'll break down the key concepts, connect them, and make sure you're feeling confident. Let's dive in!

#Hooke's Law and Springs

#The Basics

• Hooke's Law describes the force exerted by an ideal spring:

  $$F_s = -k \Delta x$$

  • $F_s$ is the spring force (a restoring force)

  • $k$ is the spring constant (stiffness of the spring)

  • $\Delta x$ is the displacement from equilibrium

• Spring Constant (k): A measure of a spring's stiffness. A smaller k means the spring is easier to stretch.

#Visualizing Hooke's Law

• Graphing: When you graph spring force ($F_s$) vs. displacement ($\Delta x$), the slope is the spring constant (k).

  

  Caption: The slope of this graph represents the spring constant, k.

#Elastic Potential Energy

• The energy stored in a spring due to its deformation:

  $$U_s = \frac{1}{2}k(\Delta x)^2$$

#Conservative Forces

#What are they?

• Conservative Force: Work done by the force is independent of the path taken. It only depends on the initial and final positions. 💡

• Dissipative Forces: Forces like friction or external applied forces where energy is lost from the system (usually as heat).

#Key Characteristics

• Path Independence: Work done is the same regardless of the path.
• Zero Work in Closed Path: Total work done around a closed path is zero.

#Examples

• Gravitational Force
• Spring Force

#Work and Potential Energy

• Work done by a conservative force is equal to the negative change in potential energy:

  $$W = -\Delta U$$

• Or, in integral form:

  $$W = \int_{a}^{b} F \cdot dr = -\Delta U$$

  

• Differential version (force as the negative gradient of potential energy):

  $$F = -\frac{dU}{dr}$$

  ![Differential Version](https://zupay.blob.core.windows.net/resources/files/0baca4f69800419293b4c75aa2870acd_eb6df2_621.png?alt=media&token...