(Solved): 7. Lord Farquaad's henchman decides to try his hand at hard maintenance. In the figure shown he ...

7. Lord Farquaad's henchman decides to try his hand at hard maintenance. In the figure shown he's using a tree-trimmer. The entire system is in equilibrium at this moment. Determine the magnitude of the force exerted on the tree at point $B$, as well as the magnitude of the reaction forces at $C$ and $D$. [Answer: $B=269\mathrm{N},C=335\mathrm{N},\mathrm{D}=200\mathrm{N}$ ] - The tree-trimmer is exerting a horizontal force on the tree branch at points $A$ and $B$. - Joints C, D, E, and F are standard pin joints. - $T$ is the tension in the cable, which is attached to the tree trimmer at $\mathrm{H}$. It goes around a pulley wheel at $\mathrm{E}$, another pulley wheel at $F$. The henchman is pulling the cable at point $P$. - Pulley wheel E has radius re. - Pulley wheel $\mathrm{F}$ has radius $\mathrm{r}$. - The mass of the tree trimmer is ${\mathrm{m}}_1$. The center of mass of the tree-trimmer is ${\mathrm{G}}_1$. - The mass of the henchman is $m_2$. The center of mass of the henchman is ${\mathrm{G}}_2$. - You may ignore the mass of bodies $BCD$ and DE. - Pulley wheel E has radius re. - Pulley wheel $\mathrm{F}$ has radius $\mathrm{r}$. - The mass of the tree trimmer is ${\mathrm{m}}_1$. The center of mass of the tree-trimmer is ${\mathrm{G}}_1$. - The mass of the henchman is $m_2$. The center of mass of the henchman is ${\mathrm{G}}_2$. - You may ignore the mass of bodies BCD and DE. - You may also ignore the mass of the pulley wheels. - The henchman is holding the tree-trimmer at point $Q$. You may treat this joint the same as you would a welded joint. - If necessary you may assume that all friction between the henchman and the ground is acting at point $R$. You may ignore any friction acting at point $\mathrm{S}$.