kokonaisenergia

Kokonaisenergia, Finnish for total energy, denotes the total energy of a physical system. In classical mechanics it is formed by the sum of kinetic energy and potential energy: E = T + V. Kinetic energy depends on motion (for a point mass, T = 1/2 m v^2), while potential energy arises from position in a force field (for example, gravitational U = mgh or a spring energy 1/2 k x^2).

In conservative systems the total energy is conserved: as a system evolves, energy continuously shifts between kinetic and potential forms, but their sum remains constant. This is visible in a swinging pendulum or an oscillating mass-spring system, where energy continuously converts between motion and elevation but does not vanish or appear from nowhere.

In relativistic physics the concept generalizes to include rest energy. The total energy of a particle satisfies E^2 = (pc)^2 + (mc^2)^2, and at low speeds E ≈ mc^2 + 1/2 mv^2, so the rest energy mc^2 is part of the kokonaisenergia. In thermodynamics and continuum mechanics, kokonaisenergia also comprises internal (thermal) energy and the kinetic energy of macroscopic motion, often expressed as E = ∫ [ρ(v^2/2 + e) + external potential terms] dV for a continuous medium.

Applications of kokonaisenergia span education, engineering, and physics research, providing a unifying framework to analyze motion, forces, and energy flows. In quantum mechanics, the Hamiltonian operator represents the total energy, with its eigenvalues corresponding to possible kokonaisenergia states of a system. The concept thus bridges mechanics, thermodynamics, relativity, and quantum theory.