11.1:
Work
Work results when a force acting on an object displaces it. It is equal to the product of the scalar component of force along the displacement direction.
Mathematically, work can be given as the dot product of the applied force and the displacement of the object.
The SI unit of work is the joule. One joule is the work done when a one-newton force displaces an object by one meter.
Since work is a scalar quantity, its magnitude can be positive, negative or zero depending on the direction of the force relative to the displacement.
Consider the example of a crane lifting a load upward. Here, the applied force and displacement vectors are aligned in the same direction, so the work done is positive.
In another example, when brakes are applied to a moving car, the braking force acts in the opposite direction to the car's motion. Here, the work done is negative.
A frictionless pulley lifting a load through a massless inextensible string does zero work as force and displacement are perpendicular.
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.
Leitura Sugerida
- Hibbeler, R.C. (2016). Engineering Mechanics: Statics. Fourteenth Edition, New Jersey: Pearson. Section 11.1, Pp. 581-582.
- Meriam, J.L., Kraige, L.G. and Bolton, J.N. (2016). Engineering Mechanics: Statics and Dynamics. Eighth Edition, Singapore: John Wiley & Sons. Section 7.2 Pp. 392-393.
- Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. and Self, B.P. (2016). Vector Mechanics For Engineers. Eleventh Edition, New York: McGraw-Hill Education. Section 10.1A Pp. 575.