Mechanical energy

The mechanical energy is a quantity used in traditional Mécanique to indicate the energy of a Système stored in the form of kinetic energy and of mechanical potential energy. It is a preserved quantity in the absence of Frottement or of Choc and proves for that practices to use.

Expression

The mechanical energy is generally expressed:

E_m = E_c + E_p

where:

$E_m$ is the mechanical energy
$E_c$ is the kinetic energy
$E_p$ is the potential energy

Specific solid

For a specific solid M the mechanical potential energy is given by its Position and the kinetic energy by its Speed. There is thus

E_m = \ frac {1} {2} mv^2 + V (M)

where:

$m$ is the Masse solid
$v$ is the Speed center of gravity;
$V$ is the Potentiel mechanics on the level of the point $M$

Nondeformable extended solid

For a nonspecific indeformable solid, it is advisable to add the kinetic energy of Rotation. The potential energy is given, in the case of a potential Gravitation nel, by the position of the center of gravity G .

E_m = \ frac {1} {2} mv^2 + \ frac {1} {2} J \ Omega ^2 + V (G)

where, all equal notations in addition

$J$ is the Moment of inertia solid compared to its axis of rotation;
$\ Omega$ is its angular Velocity of rotation.

Deformable solid

For a deformable solid, intervene of the terms of deformation (tension, Torsion, Contraction) as well in the kinetic energy as the mechanical potential energy.

Conservation

The mechanical energy of a system subjected to conservative forces, i.e. drifting of a Potential , is preserved.

See too

The mechanical energy is not a Invariant galiléen and thus depends on the selected reference frame.

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