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:


force decomposition in its cartesian components

Taking into account the definition of vector magnitude, the magnitude of the force F is obtained throughout the following expression:


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:


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

force decomposition according quadrants
Experiment & Learn
Force vector decomposition

Drag the red point in order to change the force vector 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 Fx and Fy set over the coordinate axes, whose action together is equivalent 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

Now... ¡Test yourself!

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