Mechanical Energy - General

General

Energy is a scalar quantity and the mechanical energy of a system is the sum of the potential energy which is measured by the position of the parts of the system, and the kinetic energy which is also called the energy of motion:

The potential energy, U, depends on the position of an object subjected to a conservative force. It is defined as the object's ability to do work and is increased as the object is moved in the opposite direction of the direction of the force. If F represents the conservative force and x the position, the potential energy of the force between the two positions x₁ and x₂ is defined as the negative integral of F from x₁ to x₂:

The kinetic energy, K, depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them. It is defined as one half the product of the object's mass with the square of its speed, and the total kinetic energy of a system of objects is the sum of the kinetic energies of the respective objects:

The law of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the total mechanical energy of that body or system remains constant. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path. On the contrary, when a non-conservative force acts upon an object, the work done by the non-conservative force is dependent of the path.