Mechanical energy

The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical energy is constant.

In all real systems, however, nonconservative forces, such as frictional forces, will be present, but if they are of negligible magnitude, the mechanical energy changes little and its conservation is a useful approximation.

The equivalence between lost mechanical energy and an increase in temperature was discovered by James Prescott Joule.

The potential energy, U, depends on the position of an object subjected to gravity or some other conservative force.

[nb 1][1] 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:[4]

The principle of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the mechanical energy of that body or system remains constant.

[11][12] According to the principle of conservation of mechanical energy, the mechanical energy of an isolated system remains constant in time, as long as the system is free of friction and other non-conservative forces.

In any real situation, frictional forces and other non-conservative forces are present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation.

[1][13] In a mechanical system like a swinging pendulum subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible, energy passes back and forth between kinetic and potential energy but never leaves the system.

The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point.

On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points.

However, when taking the frictional forces into account, the system loses mechanical energy with each swing because of the negative work done on the pendulum by these non-conservative forces.

[2] That the loss of mechanical energy in a system always resulted in an increase of the system's temperature has been known for a long time, but it was the amateur physicist James Prescott Joule who first experimentally demonstrated how a certain amount of work done against friction resulted in a definite quantity of heat which should be conceived as the random motions of the particles that comprise matter.

[14] This equivalence between mechanical energy and heat is especially important when considering colliding objects.

In an elastic collision, mechanical energy is conserved – the sum of the mechanical energies of the colliding objects is the same before and after the collision.

After an inelastic collision, however, the mechanical energy of the system will have changed.

The collision can be described by saying some of the mechanical energy of the colliding objects has been converted into an equal amount of heat.

from the centre of Earth possesses both kinetic energy,

, (by virtue of its motion) and gravitational potential energy,

If the satellite is in circular orbit, the energy conservation equation can be further simplified into

These devices can be placed in these categories: The classification of energy into different types often follows the boundaries of the fields of study in the natural sciences.