Unit 3 · 3.3 — Potential Energy

Everything to learn here

• Concept: Potential energy is stored energy internal to a system due to the configuration or relative positions of interacting objects (requires a system of at least two objects, e.g., an object-Earth system).
• Concept: A single isolated object cannot possess potential energy by itself; potential energy is a property of a system of at least two interacting bodies.
• Concept: The choice of the zero-reference level for potential energy is arbitrary; only the change in potential energy (delta U) determines physical motion and dynamics.
• Equation: $$\Delta U_g=mgh\text{(Change in Gravitational Potential Energy near Earth’s surface)}$$
• Equation: $$U_G=-G{m}_1\frac{m_2}{r}\text{(Universal Gravitational Potential Energy; zero is defined at infinite distance in an astronomical context)}$$
• Equation: $$U_s=\frac{1}{2}k{x}^2\text{(Elastic Potential Energy stored in an ideal spring)}$$
• Vocabulary: Conservative Force — A force (like gravity or spring force) where the work done is independent of the path taken and mechanical energy is fully recoverable.
• Vocabulary: Nonconservative Force — A force (like kinetic friction or air resistance) whose work depends on the path taken, typically converting macroscopic mechanical energy into microscopic thermal energy.
• Skill: Translation Between Representations — Drawing a potential energy curve (U vs. x) and interpreting the negative of its slope as the restoring force.
• Skill: System Framing — Explicitly defining the system boundary to determine whether gravity does external work on a single object or acts as internal potential energy within an object-Earth system.
• Concept: The reference point for zero potential energy is an arbitrary choice made by the observer to simplify the mathematical analysis.
• Concept: The total potential energy of a system is found by summing the potential energies of every unique pair of interacting objects.
• Concept: Systems containing objects that interact through conservative forces or change shape reversibly can store both kinetic and potential energies.

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