Definitions and units

Work is done when a force is applied to an object, and the object moves in the direction of the applied force.
The mathematical formula for work is W = F × d × cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement.
The SI unit of work is the joule (J), where 1 joule = 1 newton × 1 meter.
Positive work occurs when the force and displacement are in the same direction.
Negative work occurs when the force and displacement are in opposite directions.
If there is no displacement, or the force is perpendicular to the displacement, the work done is zero.
Work is a scalar quantity and has only magnitude, not direction.
Energy is the capacity to do work.
The SI unit of energy is also the joule (J).
Kinetic energy (KE) is the energy possessed by a body due to its motion, given by KE = ½ mv², where m is mass and v is velocity.
Potential energy (PE) is the energy possessed by a body due to its position or configuration, given by PE = mgh, where m is mass, g is gravitational acceleration, and h is height.
Mechanical energy is the sum of kinetic and potential energy in a system.
Conservation of Energy states that energy can neither be created nor destroyed; it can only change forms.
The Work-Energy Theorem states that the work done on an object is equal to the change in its kinetic energy.
Power is the rate at which work is done or energy is transferred.
The formula for power is P = W/t, where W is work and t is time.
The SI unit of power is the watt (W), where 1 watt = 1 joule/second.
A higher power indicates that more work is done in less time.
Instantaneous power is the power at a specific moment, calculated as P = F × v (force times velocity).
The kilowatt-hour (kWh) is a unit of energy commonly used in electricity billing, where 1 kWh = 3.6 × 10⁶ joules.
Renewable energy sources like solar and wind power are vital for sustainable development.
Non-renewable energy sources include coal, oil, and natural gas.
Energy can exist in various forms: mechanical, thermal, chemical, electrical, nuclear, and radiant energy.
The concept of efficiency measures how effectively energy is converted to useful work, given by Efficiency (%) = (Useful energy output / Total energy input) × 100.
Gravitational potential energy depends on the mass, height, and gravitational acceleration of an object.
Elastic potential energy is stored in stretched or compressed springs, given by PE = ½ kx², where k is the spring constant and x is the displacement.
Heat energy is the result of the movement of particles within a substance and is often a byproduct of work.
Work done by a variable force can be calculated by integrating the force over the displacement: W = ∫F(x) dx.
Work done in a circular motion over a complete cycle is zero if the force is centripetal.
The mechanical advantage of a system determines how much a machine amplifies force.
Potential energy is associated with conservative forces like gravity, while non-conservative forces like friction dissipate energy.
Work done against frictional forces is converted into heat energy.
The concept of power output is critical in understanding engines and electrical devices.
The rate of energy transfer depends on the efficiency of the system.
Energy transformations play a key role in all mechanical systems, such as cars and power plants.
Renewable and non-renewable energy sources are distinguished based on their rate of replenishment.
The conservation of mechanical energy is valid in systems with no non-conservative forces acting.
Electrical power is calculated as P = IV, where I is the current and V is the voltage.
Thermal power measures the rate of heat transfer and is crucial in thermodynamic systems.
Work-energy relation connects the mechanical energy of a system with the work done by external forces.
The joule is named after James Prescott Joule, who contributed significantly to the study of energy.
Energy efficiency is a key parameter in engineering and environmental studies to minimize waste.
The concept of work and energy is foundational to understanding simple machines like pulleys and levers.