Definition of Work and Energy
In physics, work is defined as the act of applying a force on an object that results in its displacement in the direction of that force. Mathematically, this relationship is expressed as W = F × s × cos θ, where W represents the work done (in joules), F is the force applied (in newtons), s is the displacement (in meters), and θ is the angle between the force and displacement vectors. To achieve work, three conditions must be satisfied: a force has to be applied, displacement must occur, and the force must have a component in the direction of that displacement.
Work can be categorized into three types: positive work, where the force and displacement are in the same direction; negative work, where they are in opposite directions; and zero work, where the force is perpendicular to the displacement or no displacement occurs.
Energy, on the other hand, is defined as the capacity to do work. It shares the same units as work, measured in joules for the SI system. Energy exists in various forms, primarily kinetic energy (KE), which is the energy of a moving object and is calculated using the formula KE = (1/2)mv², where m is the mass and v is the velocity; and potential energy (PE), which is the energy held by an object due to its position or configuration, expressed as PE = mgh, with h being the height above a reference point.
Moreover, mechanical energy is the total of kinetic and potential energy in a system, illustrating the conservation of energy, which states that energy cannot be created or destroyed but only transformed from one form to another. This principle is encapsulated in the work-energy theorem, asserting that the work done on an object equals the change in its kinetic energy.