Two cables BG and BH are attached to the frame ACD as shown.Knowing that the tension in cable BG is 450N, determine the components of the force exerted by cable BG on the frame at B.

Two cables BG and BH are attached to the frame ACD as shown.Knowing that the tension in cable BG is 450N, determine the components of the force exerted by cable BG on the frame at B.

Question
Complex numbers
asked 2020-12-24

Two cables BG and BH are attached to the frame ACD as shown.Knowing that the tension in cable BG is 450N, determine the components of the force exerted by cable BG on the frame at B.
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Answers (1)

2020-12-25
From fig
\(\displaystyle{O}{B}={1}{i}+{1.5}{k}\)
\(\displaystyle{O}{G}={1.85}{j}+{0.7}{k}\)
\(\displaystyle{B}{G}={O}{G}-{O}{B}=-{i}+{1.85}{j}-{0.8}{k}\)
\(\displaystyle{\left|{B}{G}\right|}=\sqrt{{{1}^{{2}}+{1.85}^{{2}}+{0.8}^{{2}}}}={2.25}\)
\(\displaystyle\lambda={\frac{{{B}{G}}}{{{\left|{B}{G}\right|}}}}={\frac{{-{i}+{1.85}{j}-{0.8}{k}}}{{{2.25}}}}\)
\(\displaystyle\vec{{{F}}}={F}\times\lambda\)
Where F=450 N
Find \(\displaystyle\vec{{{F}}}\)
But, \(\displaystyle\vec{{{F}}}={F}_{\xi}+{F}_{{y}}{j}+{F}_{{z}}{k}\)
\(\displaystyle\vec{{{F}}}={450}\times{\left({\frac{{-{i}+{1.85}{j}-{0.8}{k}}}{{{2.25}}}}\right)}\)
\(\displaystyle=-{200}{i}+{370}{j}-{160}{k}\)
\(\displaystyle{F}_{{x}}=-{200}\) N
\(\displaystyle{F}_{{y}}={370}\) N
\(\displaystyle{F}_{{z}}=-{160}\) N
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