Detailed Summary
Work
Work occurs when a force causes a displacement in an object. The mathematical expression for work is given by the formula W = F × s × cos θ, where W represents work (in joules), F is the force applied (in newtons), s is the displacement (in meters), and θ is the angle between the force and the direction of motion. Work can be categorized as positive, negative, or zero based on the direction of the force in relation to the displacement.
Energy
Energy is defined as the capacity to perform work, measured in joules. Two prominent forms of energy include kinetic energy (KE), calculated by KE = (1/2)mv², and potential energy (PE), expressed as PE = mgh. Here, m denotes mass in kilograms, v is velocity in meters per second, g represents the acceleration due to gravity (~9.8 m/s²), and h is the height above a reference point.
Mechanical Energy
Mechanical energy is the total energy of a system, which is the sum of kinetic and potential energies. Importantly, in a closed system devoid of external forces, mechanical energy remains constant, allowing for energy transformation between forms without loss.
Power
Power depicts the rate at which work or energy transfer occurs, with the formula P = W/t where P is power (in watts), W is work done, and t is the time taken. The relationship between power and energy can also be expressed as P = E/t.
Work-Energy Theorem and Conservation of Energy
The work-energy theorem states that the work done on an object corresponds to its change in kinetic energy. Moreover, the law of conservation of energy asserts that energy cannot be created or destroyed but only transformed from one form to another, emphasizing the continuity of total energy in a closed system.