Whether you are in the midst of a workday or just dreaming about it, you probably consider your job to be a source of energy. You may also think about the skills, knowledge and wisdom you gain from your work. And the ways it has changed you – perhaps by teaching you to be disciplined or by encouraging you to believe in yourself, or by giving you experiences and relationships you would not have had otherwise. Perhaps you even consider the ways in which your work has helped other people. But what does work actually do? And how do you measure it?
If you have ever taken a physics class, you have likely heard a teacher explain that the concept of work is based on the idea that any object in motion gains energy. The increase in an object’s energy is directly proportional to the force exerted on it and the distance the object moves. The SI unit for work is the joule, named after 19th century English physicist James Prescott Joule, and is equal to the product of force and displacement. Other nonstandard units for work include the newton-meter, the erg, and the foot-pound. Since work is a form of energy, it is often measured in the same units as that quantity.
Work can only be done on an object if there is some kind of displacement, or “d,” and the force is applied for a certain amount of time, or “t.” The direction the force is directed in must also be considered, since if the force is perpendicular to the motion, no work is done.
A number of things we do in everyday life, such as lifting a heavy object or swinging it around a circular path, are examples of work. But some things that seem to do work in everyday circumstances are not true work in the scientific sense. For example, the person holding a briefcase does not do any work on it, even though he or she feels tired, because the forces are not parallel to the displacement.
In addition, the direction in which the force is exerted must also be considered when calculating work. The force can be either constant or variable, but the displacement must always be one-way and the direction of motion must be perpendicular to the direction in which the force is being applied. The definite integral of power over time is the quantity that determines work. This can be found by dividing an appropriate angular acceleration formula by the tangential velocity of the body. This is a path independent quantity, meaning that it is the same when the body is positioned along any path. This makes it easy to calculate the quantity of work done by a constant-force, constant-distance force. However, a different expression is needed for a variable-force, variable-distance, or varying-displacement force, such as the integral of power over a path. This requires the use of complex numbers, but can be easily simplified to a straight line integral by using the cosine function.