Work, Energy and Power

The Physical Concept of Work and the Work-Energy Theorem

In everyday speech, people use the word work to describe any activity that requires mental or physical effort. In physics, however, work has a precise scientific definition. Work is the energy transferred by a force acting on an object as the object undergoes a displacement; the force can do positive or negative work depending on its direction relative to that displacement. For a force to do work, the object must undergo a displacement with a component parallel or antiparallel to that force. If you push firmly against a heavy stationary wall, you may feel tired, but because the displacement of the object is zero, no work is done on the wall regardless of the magnitude of the applied force.

The mathematical formula for work done by a constant force is work equals force times displacement times the cosine of the angle between them. Work is a scalar quantity possessing magnitude but no direction. The SI unit of work is the joule, where one joule is equivalent to one newton-meter. When expressed in base SI units, one joule equals one kilogram meter squared per second squared. Because the formula includes the cosine of the angle between the force vector and the displacement vector, the direction of the force relative to the motion dictates how much work is accomplished.

Depending on that angle, work can be positive, negative, or zero. Positive work is done when the force has a component in the same direction as the displacement. Negative work is done when the force has a component directed opposite to the displacement. For instance, when an object slides across a surface, kinetic friction opposes sliding relative to the contacting surface; therefore, kinetic friction does negative work when it acts opposite the object's displacement. Furthermore, a force acting perpendicular to the direction of motion does zero work because the cosine of ninety degrees is zero. A prime example is centripetal force, which performs zero work on an object in uniform circular motion because it is perpendicular to the velocity vector.

Work directly alters the motion of an object according to the work-energy theorem. The work-energy theorem states that the net work done on an object equals its change in kinetic energy. When positive net work is done on an object, its kinetic energy and speed increase. Conversely, when negative net work is done on an object, its kinetic energy and speed decrease. If the net work done over an interval is zero, the object's kinetic energy is the same at the beginning and end of that interval, though it may change in between.