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

$E\_m\; =\; \backslash \; frac\; \{1\}\; \{2\}\; mv^2\; +\; V\; (M)$

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 .

$E\_m\; =\; \backslash \; frac\; \{1\}\; \{2\}\; mv^2\; +\; \backslash \; frac\; \{1\}\; \{2\}\; J\; \backslash \; Omega\; ^2\; +\; V\; (G)$

where, all equal notations in addition

• $J$ is the Moment of inertia solid compared to its axis of rotation;
• $\backslash \; Omega$ 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

• kinetic Energy ~ Energy ~ mechanical potential Energy
• conservative Force

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

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