Sometimes, when we study the force acting on a body, it can be interesting to decompose it into several forces, each of them with the direction of the cartesian axis, in sucha a way the effect of all of them is equivalent to the force decomposed. As we study on the section vectors representation, on the plan OXY we get that:

$\stackrel{\to }{F}=\stackrel{\to }{{F}_{x}}+\stackrel{\to }{{F}_{y}}={F}_{x}·\stackrel{\to }{i}+{F}_{y}·\stackrel{\to }{j}$

Taking into account the definition of vector magnitude, the magnitude of the force $\stackrel{\to }{F}$ is obtained throughout the following expression:

$F=\sqrt{{{F}_{x}}^{2}+{{F}_{y}}^{2}}$

Throughout the definition of tangent of an acute angle we can relate the magnitudes Fx and Fy to the angle α that take place to with the half turn X positive on the following way:

$\mathrm{tan}\left(\alpha \right)=\frac{{F}_{y}}{{F}_{x}}$

Additionally we can relate these magnitudes to the lower angle that make $\stackrel{\to }{F}$ with the X axis, pointing to the sector of the system of reference in which it is located:

Experiment & Learn

Data

Force vector decomposition

Drag the red point in order to change the force vector $\stackrel{\to }{F}$ from the figure. Watch how the value of its magnitude F decrese by making it smaller, and increase by making it bigger. The bigger magnitude, the higher force intensity.

Check how it can be decomposed into two forces $\stackrel{\to }{{F}_{x}}$ and $\stackrel{\to }{{F}_{y}}$ set over the coordinate axes, whose action together is equivalent to $\stackrel{\to }{F}$. The value of the mgnitudes of these two forces are obtained throughout the use of the sine and cosine definition over the triangle rectangle which is formed, in such a way:

Fx = F · cos (α) = valor
Fy = F · sin(α) = valor