Mechanics

Decomposition of forces

Decomposition of forces into two perpendicular components Fx and Fy

There are situations in which it may be advantageous to replace one force    with two other perpendicular forces, that is, to decompose    into perpendicular component forces, as we do when working with vectors in general.

Let’s take, for example, the case of the force  in the figure above. Let’s decompose this force into two component forces about the perpendicular x and y directions. In this way, we can say that:

That is, the force  is the resultant of  e  . This means that the forces  and  , acting together, produce the same effect as the force  acting alone. Therefore, the force  in the figure above can be replaced by the force pair   and  .


If we consider the uncolored right triangle in the figure above, we have the following relationship:


Always remembering that:

– Since α and β are complementary (α + β = 90º), we have: 

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