(Solved): Determine the equivalent force-couple system at the center O for each of the three cases of forces ...

Determine the equivalent force-couple system at the center $O$ for each of the three cases of forces $(F=590\mathrm{N})$ being applied along the edges of a regular hexagon of width $d=250\mathrm{mm}$. The couple is positive if counterclockwise, negative if clockwise. Next, for each case, replace the original system with a single equivalent force located along the $y$-axis. Determine the distance $y$. Your answer will be positive if above point $O$, negative if below. (a) Answers: Force-Couple System at $O$ (a) $\mathbf{R}=$ ( (b) $\mathbf{R}=$ ( (c) $\mathbf{R}=($ $\mathbf{i}+$ i + i + j) $\mathrm{N},{\mathrm{M}}_{\mathrm{O}}=$ j) $\mathrm{N},{\mathrm{M}}_{\mathrm{O}}=$ j) $\mathrm{N},{\mathrm{M}}_{\mathrm{O}}=$ $N?m$ $N?m$ $\mathrm{N}?\mathrm{m}$ Single equivalent force (a) $y=$ $\mathrm{mm}$ (b) $y=$ $\mathrm{mm}$ (c) $y=$ $\mathrm{mm}$