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Work can be calculated from the formula:
(Readers not familiar with vectors and calculus please see "Simpler Formulae" below.)
Work is a scalar quantity, but it can be positive or negative.
Not all forces do work. For instance, a centripetal force in uniform circular motion does not transfer energy; the speed of the object undergoing the motion remains constant. This fact is confirmed by the formula: if the vectors of force and displacement are perpendicular, their dot product is zero.
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.
Heat conduction from a warmer body to a colder one is not normally considered to be a form of mechanical work, because at the macroscopic level, there is no measurable force. At the atomic level, there are forces as the atoms collide, but they average to nearly zero in bulk.
The SI derived unit of work is the Joule, which is defined as the work done by a force of one newtonThis article is about the SI unit of force. For other uses see Newton (disambiguation In physics, the newton (symbol: N) is the SI unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics. It was adopted by the General acting over a distance of one metreFor other uses of "metre" and "meter", see Metre (disambiguation). The metre is the basic unit of length in the International System of Units (SI: Systeme International d'Unites). It is defined as the length of the path travelled by light in absolute vacu in the direction of the force.
Non-SI units of work include the ergAn erg is the unit of energy in the centimetre-gram-second ( CGS) system of units, symbol "erg". The erg is a quite small unit, equal to 1 × 10-7 joules. It is thus equal to one gram· centimetre2/ second2. Erg is also a common name for an indoor rower, pa, the foot-poundIn physics, a foot-pound is the Imperial and U. customary unit of mechanical work, or energy, although in scientific fields one commonly uses the equivalent metric unit of the Joule (J). There are approxmately 1. 356 J per foot-pound. To calculate a foot-, and the foot-poundal .
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
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 productIn mathematics, the dot product (also known as the scalar product and the inner product is a function (·) : V × V → F, where V is a vector space and F its underlying field. In other words, it maps a pair of vectors to a scalar. When the latter term i:
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 differentialsIn mathematics differential has various meanings. In calculus, a differential is an infinitesimal change in the value of a function. Differentials help to constitute derivatives and integrals. Outside of this context, they occur as elements of cotangent s to express the infinitesimal work done by the force over an infinitesimal time, thus:
The integrationThis article deals with the concept of an integral in mathematical calculus. For other meanings of "integral" see integration. In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. Unlike the process of differe of both sides of this equation yields the most general formula, as given above.
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