Cards | 10 |

Focus | Energy, Work, & Power |

Topics | Conservation of Mechanical Energy, Gravitational Potential Energy, Joules, Kinetic Energy, Potential Energy, Work, Work-Energy Theorem |

As an object falls, its potential energy is converted into kinetic energy. The principle of conservation of mechanical energy states that, as long as no other forces are applied, total mechanical energy (PE + KE) of the object will remain constant at all points in its descent.

Gravitational potential energy is energy by virtue of gravity. The higher an object is raised above a surface the greater the distance it must fall to reach that surface and the more velocity it will build as it falls. For gravitational potential energy, **PE = mgh** where m is mass (kilograms), h is height (meters), and g is acceleration due to gravity which is a constant (**9.8 m/s ^{2}**).

The Joule (J) is the standard unit of energy and has the unit \({kg \times m^2} \over s^2\).

Kinetic energy is the energy of movement and is a function of the mass of an object and its speed: \(KE = {1 \over 2}mv^2\) where m is mass in kilograms, v is speed in meters per second, and KE is in joules. The most impactful quantity to kinetic energy is velocity as an increase in mass increases KE **linearly** while an increase in speed increases KE **exponentially**.

Potential energy is the energy of an object by virtue of its position relative to other objects. It is energy that has the potential to be converted into kinetic energy.

Work is accomplished when force is applied to an object: **W = Fd** where F is force in newtons (N) and d is distance in meters (m). Thus, the more force that must be applied to move an object, the more work is done and the farther an object is moved by exerting force, the more work is done.

The work-energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. Simply put, work imparts kinetic energy to the matter upon which the work is being done.