Determine the components of F that act along rod AC and perpendicular to it. Point B is located 3 m along the rod from end C .

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Accepted Answer

[latex]\begin{aligned}& r _{C A}=3 i -4 j +4 k \&r_{C A}=6.403124\end{aligned}[/latex]

[latex]r _{C B}=\frac{3}{6.403124}\left( r _{C A} ight)=1.40556 i -1.874085 j +1.874085 k[/latex]

[latex]\begin{aligned}r _{O B} &= r _{O C}+ r _{C B} \&=-3 i +4 j + r _{C B} \&=-1.59444 i +2.1259 j +1.874085 k\end{aligned}[/latex]

[latex]\begin{aligned}r _{O D} &= r _{O B}+ r _{B D} \r _{B D} &= r _{O D}- r _{O B}=(4 i +6 j )- r _{O B} \&=5.5944 i +3.8741 j-1.874085 k\end{aligned}[/latex]

[latex]r_{B D}=\sqrt{(5.5944)^2+(3.8741)^2+(-1.874085)^2}=7.0582[/latex]

[latex]F =600\left(\frac{ r _{B D}}{r_{B D}} ight)=475.568 i +329.326 j -159.311 k[/latex]

[latex]r _{A C}=(-3 i +4 j -4 k ), \quad r_{A C}=\sqrt{41}[/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{(475.568 i +329.326 j -159.311 k ) \cdot(-3 i +4 j -4 k )}{\sqrt{41}}[/latex]

[latex]F_{\|}=82.4351=82.4 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=600^2-82.4351^2 \F_{\perp}=594 N\end{aligned}[/latex]

Question 2.137: Determine the components of F that act along rod AC and perp...

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