Unit 3 · Work, Energy, and Power

Translational kinetic energy ● (core concept) — The energy of an object's motion: K = ½·m·v². It is a scalar whose value depends on the observer's reference frame.

Work ● (core concept) — Energy transferred into or out of a system by a force acting over a distance. Work is a scalar that can be positive, negative, or zero; only the component of the force parallel to the displacement changes the system's energy.

Conservative force ● (core concept) — A force whose work depends only on the initial and final configurations, not the path taken. Potential energy is associated with conservative forces; examples are gravity and the spring force.

Nonconservative force ● (core concept) — A force whose work depends on the path taken, so mechanical energy is dissipated; examples are friction and air resistance.

Work-energy theorem ● (core concept) — The change in an object's kinetic energy equals the net work done on it — the sum of the work done by every force exerted on the object.

Work from a force–position graph ● (core concept) — The work done by a force over a distance equals the area under the curve of force versus position.

Potential energy ● (core concept) — Energy stored in the configuration of a system whose objects interact via conservative forces. It is a scalar, and the observer chooses the configuration where it equals zero.

Elastic potential energy ● (core concept) — Energy stored in a stretched or compressed ideal spring: U_s = ½·k·x², where x is the displacement from the spring's relaxed length.

Gravitational potential energy ● (core concept) — For two spherical masses, U_g = −G·M·m/r (zero at infinite separation). Near a planet's surface, changes simplify to ΔU_g = m·g·Δh.

Mechanical energy ● (core concept) — The sum of a system's kinetic and potential energies.

Conservation of energy ● (core concept) — Energy is conserved in all interactions. A system's total energy stays constant when no work is done on it and no nonconservative forces act within it; otherwise the change in energy equals the energy transferred into or out of the system.

Power ● (core concept) — The rate of energy transfer or conversion. Average power is P_avg = ΔE/Δt = W/Δt; the instantaneous power from a constant force is P = F_∥·v, using the force component parallel to the velocity.