Determine the components of F that act along rod AC and perpendicular to it. Point B is located at the midpoint of the rod.

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Accepted Answer

[latex]r _{A C}=(-3 i +4 j -4 k ), \quad r_{A C}=\sqrt{(-3)^2+4^2+(-4)^2}=\sqrt{41} m[/latex]

[latex]r _{A B}=\frac{ r _{A C}}{2}=\frac{-3 i +4 j +4 k }{2}=-1.5 i +2 j -2 k[/latex]

[latex]\begin{aligned}r _{A D} &= r _{A B}+ r _{B D} \r _{B D} &= r _{A D}- r _{A B} \&=(4 i +6 j -4 k )-(-1.5 i +2 j -2 k ) \&=\{5.5 i +4 j -2 k \} m\end{aligned}[/latex]

[latex]r_{B D}=\sqrt{(5.5)^2+(4)^2+(-2)^2}=7.0887 m[/latex]

[latex]F =600\left(\frac{ r _{B D}}{r_{B D}} ight)=465.528 i +338.5659 j -169.2829 k[/latex]

[latex] ext { Component of } F ext { along } r _{A C} ext { is } F _{\|}[/latex]

[latex]F_{\|}=\frac{ F \cdot r _{A C}}{r_{A C}}=\frac{(465.528 i +338.5659 j -169.2829 k ) \cdot(-3 i +4 j -4 k )}{\sqrt{41}}[/latex]

[latex]F_{||}=99.1408=99.1 N[/latex]

[latex] ext { Component of } F ext { perpendicular to } r _{A C} ext { is } F_{\perp}[/latex]

[latex]\begin{aligned}&F_{\perp}^2+F_{\mid \mid}^2=F^2=600^2 \&F_{\perp}^2=600^2-99.1408^2 \&F_{\perp}=591.75=592 N\end{aligned}[/latex]

Question 2.136: Determine the components of F that act along rod AC and perp...

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