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Work (abbreviated W) is the energy transferred in
applying force over a distance. It is given by the formula:
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- F is the force.
- s is the distance.
Work is a scalar quantity, but it can be positive or negative.
Forms of work that are not evidently mechanical, such as electrical work, can be considered as special cases of this principle; for instance, in the
case of electricity, work is done on charged particles moving through
a medium.
The SI derived unit of work is the Joule, which is defined as the work done by a force of one newton acting
over a distance of one meter. Other units include the erg, the foot-pound, and the foot-poundal.
Simpler formulas
In the simplest case, that of a body moving in a constant direction, acted on by a force parallel to the direction of motion,
the work is given by the formula
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where F is the force and s is the distance traveled by the object. The work is taken to be negative when the
force opposes the motion. More generally, the force and distance are taken to be vector quantities, and combined using the dot
product:
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This formula holds true even when the force acts at an angle to the distance traveled. To further generalize the formula to
situations in which the force and the object's direction of motion changes over time, it is necessary to use differentials to express the infinitesimal work
done by the force over an infinitesimal time, thus:
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The integration of both sides of this equation yields the most general formula,
as given above.
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