W = F * CosΘ * s
The work performed is composed of two vectors, which are: Force (F) and Displacement (s). This means that work is the scalar productof these two vectors. Since we consider the direction too, besides the magnitude, in a vector, we have to take into account that for these two vectors (force and displacement) there is also adirection, which it is going to be represented in the formula as the angle (Θ) that is formed between them.
Since we know that work only depends on its starting and ending position, we have as a fact thatwork is a scalar quantity, which means that the direction is not relevant, work does not have an ascertained direction, even though it is formed by two vectors.
From all the above information, wefinally gathered that to have work, we must have two important elements. There must exist force acting on the object, and there must exist a displacement of the final position of the object. It is veryimportant that both elements are present to perform work, if one of them is missing, no work will be performed.
When performing an operation regarding work, on this chapter, you are going to see adrawing like this: Y
N Fy F
fk Θ X
The picture shows forces being applied to an object on a horizontal surface, thedisplacement (s) is not shown in the picture, but usually the magnitude will be given on the problem. We can notice that there is a force (F) applied to the object at a certain angle (Θ), which opens force ony-axis (Fy) and force on x-axis (Fx). We also see kinetic friction (fk), Normal force (N), and Weight (W).
Now, we’re going to show some examples that will help to have a better understanding aboutthe performing of work and the importance of its elements (force and displacement):
* If there is no displacement on the object, no work will be done.
S = 0, then W = 0
If you are pushing...