Conservation of Energy

Objective: Apply K + U conservation when nonconservative transfer is negligible.

Mechanical energy is the sum of selected kinetic and potential energies, commonly E_mech = K + U_g + U_s. If a system experiences negligible friction, drag, and external work, its mechanical energy can be approximately constant. For a falling object, a decrease in gravitational potential energy accompanies an increase in kinetic energy. Starting at rest 5 m above a chosen zero level, the ideal model gives K = mgh immediately before reaching that level, provided other stores are negligible. The total energy of an appropriately enlarged system remains conserved even when mechanical energy changes. The assumptions and reference level must be stated.

Objective: Account for mechanical-energy decrease in real processes.

Friction and drag often transfer organized mechanical energy into internal energy of contacting surfaces and surrounding fluid. If a sliding block begins with 40 J of kinetic energy and stops after a 30 J transfer to surfaces by friction, another 10 J must be accounted for by additional transfer or energy storage; one cannot simply claim the block stopped under only that 30 J loss. The work done by kinetic friction on a sliding object is negative relative to its displacement in the simple horizontal case. Heating is a transfer description; a rise in thermal/internal energy is a state change. Sound can carry some energy away. Complete accounting specifies the system boundary and relevant pathways.

Objective: Distinguish a device, its surroundings, and a larger system.

Energy conservation is a general accounting principle, but a selected subsystem can gain or lose energy across its boundary. For a cart alone, an external push can increase K; for cart plus person, chemical energy changes and energy may disperse thermally. An isolated idealized system has no exchange with its surroundings, while a closed system is often defined as no matter exchange and may still exchange energy. In a power station, fuel or sunlight is an input and electrical and thermal outputs must be traced; a simple useful-efficiency percentage does not close the whole balance. Define initial and final states, boundaries, and units before deciding whether energy has been accounted for.