Work and Energy Systems

This comprehensive page explores the fundamental concepts of work, energy, and their applications in both open and closed systems, with special emphasis on spring mechanics and energy conservation.

Definition: Work is defined as the product of force and displacement $W = F·d$, where the angle between force and displacement determines if work is positive, negative, or zero.

Vocabulary: Kinetic Energy (KE) represents motion energy (½mv²), while Potential Energy (PE) represents stored energy (mgh for gravitational PE).

Example: In spring systems, maximum potential energy occurs at maximum compression or extension, while maximum kinetic energy occurs at the equilibrium position.

Highlight: In closed systems, energy is conserved with PE and KE transforming between each other (ΔPE = -ΔKE), while open systems involve external forces affecting total energy.

Quote: "At equilibrium, acceleration is zero and velocity is maximum; far from equilibrium, acceleration is maximum and velocity is zero."

The page includes detailed graphs showing the relationships between position, velocity, and energy in various scenarios, particularly emphasizing spring motion and free fall situations. The mathematical treatment includes Hooke's law $F=-kx$ for spring forces and the conservation of mechanical energy (ME=KE+PE) in closed systems.