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In addition, not all forces do work. For instance, a Centripetal Force in uniform Circular Motion does not (because as seen from the above definition scalar product of force and displacement vector is zero because they are ortogonal); the Kinetic Energy of the object undergoing the motion remains constant (because no force is acting on it). DEFINITION ''Note: Readers not familiar with Multivariate Calculus or Vectors , please see "Simpler formulae" below.'' Work is defined as the following Line Integral : : where: C : is the Force vector; : is the Position Vector . This formula readily explains how a nonzero force can do zero work. The simplest case is where the force is always perpendicular to the direction of motion, making the Integrand always zero (viz. circular motion). However, even if the integrand sometimes takes nonzero values, it can still integrate to zero if it is sometimes negative and sometimes positive. The possibility of a nonzero force doing zero work exemplifies the difference between work and a related quantity: Impulse (the integral of force over time). Impulse measures change in a body's Momentum , a vector quantity sensitive to direction, whereas work considers only the magnitude of the velocity. For instance, as an object in uniform circular motion traverses half of a revolution, its centripetal force does no work, but it transfers a nonzero impulse. UNITS The SI Derived Unit of work is the Joule (J), which is defined as the work done by a force of one Newton acting over a distance of one Meter . The dimensionally equivalent Newton-meter (N·m) is sometimes used instead; however, it is also sometimes reserved for Torque to distinguish its units from work or energy. Non-SI units of work include the Erg , the Foot-pound , the Foot-poundal , and the Liter-atmosphere . SIMPLER FORMULAE In the simplest case, that of a body moving in a steady direction, and acted on by a constant force parallel to that direction, the work is given by the formula : where : ''F'' is the force and : ''s'' is the distance travelled 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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