Conservative Forces
If the vector field associated to a force is conservative then the force is said to be a conservative force.
The most prominent examples of conservative forces are the force of gravity and the electric field associated to a static charge. According to Newton's law of gravitation, the gravitational force, acting on a mass, due to a mass which is a distance away, obeys the equation
where is the Gravitational Constant and is a unit vector pointing from towards . The force of gravity is conservative because, where
is the Gravitational potential energy.
For conservative forces, path independence can be interpreted to mean that the work done in going from a point to a point is independent of the path chosen, and that the work W done in going around a closed loop is zero:
The total energy of a particle moving under the influence of conservative forces is conserved, in the sense that a loss of potential energy is converted to an equal quantity of kinetic energy or vice versa.
Read more about this topic: Conservative Vector Field
Famous quotes containing the words conservative and/or forces:
“The radical invents the views. When he has worn them out the conservative adopts them.”
—Mark Twain [Samuel Langhorne Clemens] (18351910)
“There is the falsely mystical view of art that assumes a kind of supernatural inspiration, a possession by universal forces unrelated to questions of power and privilege or the artists relation to bread and blood. In this view, the channel of art can only become clogged and misdirected by the artists concern with merely temporary and local disturbances. The song is higher than the struggle.”
—Adrienne Rich (b. 1929)