11.1 : Work

Work is a fundamental concept of mechanical engineering and has many applications. Understanding how work is calculated and the different types of work can help us better understand physical processes and provide insights into complex problems.

Work is defined as the result of a force acting on an object, causing it to move along the line of action of force. It is also defined as the process of transferring energy through the application of force on an object, resulting in its displacement. This energy transfer is responsible for the object's change in motion or position. Work can be written as the product of the force and the component of displacement in the same direction, or alternatively written as the dot product of the applied force and displacement of the object. The SI system considers one joule as its unit—this is equal to performing one newton of force over one meter of displacement.

The type of work done on an object depends upon the direction of the force relative to the displacement. If the applied force and displacement are parallel to each other, the work done is positive and if they are anti-parallel, the work done is negative. When the applied force and displacement are perpendicular to each other, the work done is zero. An example of positive work being done is when a crane lifts a heavy load—by exerting an upward force on the load, it moves up relative to ground level. Negative work occurs, for example, when brakes are applied to a moving car—the wheels exert a force opposing its motion, resulting in negative work being done on it.

Some forces, such as those acting on fixed points or perpendicular to displacement, do no work. Examples include the reaction at a frictionless pin when the supported body rotates about it, the reaction force acting on a body which is moving on a frictionless surface, etc. However, forces that do work include the weight of a body and friction force acting on a body moving on a rough surface.

In some cases, the sum of the work done by multiple forces is zero. For example, two rigid bodies connected by a frictionless pin require equal but opposite forces for movement, so their combined work is zero. Similarly, two blocks connected by an extensible cord have tension forces of equal magnitude but opposite signs, resulting in zero work.

Overall, understanding which forces produce work and how to calculate work can provide helpful insights into complex physical problems and allow us to manage these processes effectively for the desired results.