Work Energy and Power

Work

Work is done when a force acts on a body and the body undergoes a displacement in the direction of the force. It is measured as the scalar product of force and displacement vectors ($W = F \cdot s = Fs \cos\theta$).

Kinetic Energy

Kinetic energy is the energy possessed by a body by virtue of its motion. It is given by the formula $K = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.

Potential Energy

Potential energy is the stored energy in a body due to its position, configuration, or state of strain. For example, gravitational potential energy near the Earth's surface is given by $U = mgh$.

Work-Energy Theorem

The work-energy theorem states that the work done by the net force on a body equals the change in its kinetic energy ($W = \Delta K$).

Conservation of Mechanical Energy

The total mechanical energy of a system remains constant if the internal forces doing work are conservative, meaning energy only transforms between kinetic and potential forms.

Power

Power is defined as the rate at which work is done or energy is transferred. It is calculated as $P = \frac{W}{t}$ or as the dot product of force and velocity ($P = F \cdot v$).