Forces

At point G, three mutually perpendicular forces act: F₁ = 16 N, F₂ = 7 N, and F₃ = 6 N. Determine the resultant force F and the angles between F and each of F₁, F₂, and F₃.

Final Answer:

F =  18.5 N
α =  29.9515 °
β =  67.7238 °
γ =  71.0394 °

Step-by-step explanation:

$$\begin{gathered} F_1=16\text{N} \\ {F}_2=7\text{N} \\ {F}_3=6\text{N} \\ F=\sqrt{F_1^2+F_2^2+F_3^2}=\sqrt{16^2+7^2+6^2}=\sqrt{341}=18.5\text{N} \end{gathered}$$

$\alpha =\frac{180°}{\pi }\cdot \arccos (\frac{F_1}{F})=\frac{180°}{\pi }\cdot \arccos (\frac{16}{18.4662})=29.9515^{\circ }=29°57^{\prime }5"$

$\beta =\frac{180°}{\pi }\cdot \arccos (\frac{F_2}{F})=\frac{180°}{\pi }\cdot \arccos (\frac{7}{18.4662})=67.7238^{\circ }=67°43^{\prime }26"$

$\gamma =\frac{180°}{\pi }\cdot \arccos (\frac{F_3}{F})=\frac{180°}{\pi }\cdot \arccos (\frac{6}{18.4662})=71.0394^{\circ }=71°2^{\prime }22"$

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