Work is the transfer of energy that occurs when a force is exerted over a displacement. It is equal to the product of the force and the change in position (or the distance traveled). The direction of the force and the relative directions of the displacement and the motion determine whether the work is positive, negative or zero.
Work can be done on an object in a variety of ways, but it always involves the application of a force and some amount of displacement. The unit used to measure work is the newton-metre, or J (short for joule), though units usually reserved for measuring heat or energy content are sometimes employed, such as the calorie, watt, erg, and therm.
In everyday use, the term work is often applied to activities that involve sustained effort and often result in some type of physical or mental exhaustion. Examples might include writing an essay, pushing a lawn mower or pulling on a rope. However, scientifically speaking, not all such activities qualify as work. In fact, many of the things that people do every day that they consider to be work do not involve any force at all. For a task to qualify as work, there must be an act of physics that requires the expenditure of energy, and for a force to do work on an object, that object must have a certain displacement.
The displacement required for a force to do work is defined as the distance the object moves per unit of time, where the time-constant of an object’s velocity is defined by the speed at which it travels over a given distance dt. For an instant dt, the amount of work that is done on the object can be determined by calculating the slope of the curve that connects the point at which the force begins to apply and the point at which the object’s velocity reaches a constant value (v). This calculation yields an expression for the work that is performed on the object at that instant
For an object to do work, some of the force must apply to the object and all of the force must be in the direction that the object moves. In other words, the force must be parallel to the direction of motion. If the force is not parallel to the direction of motion, it does no work on the object. For example, the chain on a Fido’s collar does some work when it pulls upwards and to the right, but not much work when it only pulls upwards or downwards.
A common misunderstanding about work is that it is only done when the force is directly opposed to the direction of motion. This is not true. A more accurate and meaningful definition is that work is only done when the force causes a motion that leads to a displacement. This is why it is necessary to distinguish between the “energy” that a force has and the actual mechanical energy it imparts to an object.