Work and Energy

Fundamental Concepts


Work: Work is defined as the transfer of energy that results from applying a force over a distance. Mathematically, work (W) is equal to the force (F) applied to an object multiplied by the displacement (d) of the object in the direction of the force, or W = Fd. The SI unit for work is the joule (J).
Kinetic energy: Kinetic energy is the energy an object possesses due to its motion. Mathematically, the kinetic energy (KE) of an object with mass (m) and velocity (v) is given by KE = 1/2mv^2.
Potential energy: Potential energy is the energy that an object possesses due to its position or configuration relative to other objects. Examples of potential energy include gravitational potential energy and elastic potential energy.
Conservation of energy: The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total amount of energy in a closed system remains constant.
Mechanical energy: Mechanical energy is the sum of an object's kinetic energy and potential energy. In the absence of non-conservative forces like friction or air resistance, mechanical energy is conserved.
Power: Power is the rate at which work is done or energy is transferred. Mathematically, power (P) is equal to work (W) divided by time (t), or P = W/t. The SI unit for power is the watt (W).

Work & Energy Equations


Work (W): Work is equal to the force (F) applied to an object multiplied by the displacement (d) of the object in the direction of the force, or W = Fd.
Kinetic energy (KE): The kinetic energy (KE) of an object with mass (m) and velocity (v) is given by KE = 1/2mv^2.
Potential energy (PE): The potential energy (PE) of an object due to gravity is given by PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above a reference point.
Mechanical energy (ME): The mechanical energy (ME) of an object is the sum of its kinetic and potential energies, or ME = KE + PE.
Work-energy theorem: The work-energy theorem states that the work done on an object is equal to its change in kinetic energy. Mathematically, W = ΔKE, where ΔKE is the change in kinetic energy of the object.
Power (P): Power is the rate at which work is done or energy is transferred. Mathematically, power (P) is equal to work (W) divided by time (t), or P = W/t.