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: