Work, Energy, and Power

Work: Work is done when a force causes displacement. Work = Force × Displacement × cos θ, where θ is the angle between force and displacement.

SI Unit: Joule (J). 1 Joule = 1 N × 1 m.

Conditions for Work: Force must be applied and object must move in the direction of force.

Positive, Negative, and Zero Work: Work is positive when force and displacement are in the same direction, negative when opposite, and zero when perpendicular.

Examples: Carrying a load on level ground does zero work against gravity as displacement is horizontal.

Energy: The capacity to do work. SI unit: Joule (J).

Kinetic Energy (K.E.): Energy possessed by a body due to its motion. K.E. = ½mv².

Potential Energy (P.E.): Energy possessed by a body due to its position or configuration. Gravitational P.E. = mgh.

Mechanical Energy: Sum of kinetic and potential energy in a system.

Forms of Energy: Mechanical, heat, light, sound, electrical, chemical, nuclear, etc.

Statement: Energy can neither be created nor destroyed; it can only be transformed from one form to another.

Total Energy: The total energy of an isolated system remains constant.

Applications: Pendulum (K.E. ⇌ P.E.), hydroelectric power, renewable energy systems.

In Free Fall: P.E. decreases while K.E. increases such that total mechanical energy remains constant (ignoring air resistance).

Power: The rate of doing work or rate of transfer of energy. Power = Work/Time.

SI Unit: Watt (W). 1 Watt = 1 Joule/second.

Commercial Unit: Kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ J.

Horsepower: 1 horsepower (hp) = 746 W.

Applications: Measuring performance of engines, electrical appliances, and motors.