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# work

Work is force applied over distance. Examples of work include lifting an object against the Earth's gravitation, driving a car up a hill, and pulling down a captive helium balloon. Work is a mechanical manifestation of energy.

The standard unit of work is the joule (J), equivalent to a newton - meter (N · m). This reduces to one kilogram-meter squared per second squared (kg · m 2 /s 2 or kg · m 2 · s -2 ) in base International System of Units (SI) units. Alternatively, the erg, equivalent to a dyne - centimeter (dyn · cm), can be used to express work. One erg reduces to one gram-centimeter squared per second squared (g · cm 2 /s 2 or g · cm 2 · s -2 ) in base SI units.

To convert from joules to ergs, mulitiply by 10,000,000 (10 7 ). Conversely, multiply by 0.0000001 (10 -7 ).

For a given force F (in newtons) applied over a displacement d (in meters), the work w (in joules) is given by:

w = Fd

If, in practice, force is not applied in the same direction as the displacement that results in actual work (this is the case for a car ascending a hill, for example), the vector form of the above formula must be used. For a given force vector F (in newtons, in a specified direction) applied to an object that undergoes displacement d (in meters), the work w (in joules) is given by the dot product of the force vector and the displacement vector:

w = F · d = Fd cos q

where q is the angle between the applied force vector and the direction of the displacement that results in actual work.

The above formulas also apply for work in ergs, force magnitude in dynes, and displacement magnitude in centimeters.

Although work is usually defined in mechanical terms, it can result from the action of electric fields, magnetic fields, thermal heating, particle bombardment, and various other phenomena.

Also see energy, force, mass, newton, second, SI, and Table of Physical Units.

This was last updated in August 2008

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