Work, Energy, and Power connects forces to energy changes. The principle of conservation of energy is one of the most fundamental laws in physics and a powerful problem-solving tool.
Work done W = Fs cosθ (force × displacement × cos of angle between them). Units: joules (J = N·m). Work done against friction converts KE to thermal energy. Kinetic energy KE = ½mv². Gravitational PE = mgh (relative to reference point). Elastic PE = ½kx² (Hooke\'s law spring, k = spring constant, x = extension). Conservation of energy: total energy in an isolated system remains constant. ΔKE + ΔPE = 0 (no friction) or ΔKE + ΔPE + work against friction = 0.
Power P = W/t = ΔE/t (watts, W). Also P = Fv (force × velocity) — useful for vehicles at constant speed where driving force = resistive forces. At maximum speed: driving force = total resistive force, so acceleration = 0. Efficiency = useful energy output / total energy input × 100% = useful power output / total power input × 100%. Energy can be transferred but never created or destroyed.
Friction always opposes the direction of motion. Since work = force × displacement × cosθ, and friction acts at 180° to the displacement, cos180° = -1, making friction\'s work negative. This means friction removes kinetic energy from the system, converting it to thermal energy (heat). This is irreversible — the thermal energy cannot spontaneously convert back to ordered kinetic energy. This is why perpetual motion machines are impossible and why machines always have efficiency less than 100%.
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