QUESTION $3.(10$ Marks$)$

The soft$-$ride suspension system of the mountain bike is pinned at C and supported by the shock absorber BD$.$ The seat is designed to support a load of $\backslash (\backslash$mathrm$\{$P$\}=1500\backslash$mathrm$\{$~N$\}\backslash ).$ Pin B attaches the shock absorber BD to the suspension system, has a diameter of $7\mathrm{.}5$ mm $,$ is made of a material having a shear failure stress of $\backslash (\backslash$tau$\_\{\backslash$text $\{$Failure $\}\}=150\backslash$mathrm$\{$MPa$\}\backslash )$ and is subjected to double shear.

a$)$ Draw a Free Body Diagram of ABC $($the combined seat and soft$-$ride suspension system$)(2$ Marks$)$

b$)$ Determine the factor of safety against failure of pin B $(\backslash (\backslash$mathbf$\{8\}\backslash )$ Marks$).$