Solved problem: Finding out the angled force with axis.

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Statement

difficulty

A force is given by the following expression: $\vec{F} = 3 \cdot \vec{i} + 2 \cdot \vec{j}$ . Calculate angle of horizontal.

Solution

Knowing that:

$\vec{F} = F_{x} \cdot \vec{i} + F_{y} \cdot \vec{j} \Rightarrow \{\begin{cases} F_{x} = 3 \\ F_{y} = 2 \end{cases}$

To calculate the angle we will use the expression:

$\tan (α) = \frac{F_{y}}{F_{x}} \Rightarrow \tan (α) = \frac{2}{3} \Rightarrow α = \tan^{- 1} (0.66) \Rightarrow α = 33.69 º$

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

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