Question $4[20$ marks$]$

Figure Q$4$ shows a pulley system, where a mass $\backslash ($ M$=250\backslash$mathrm$\{$Kg$\}\backslash )$ is being lifted by an applied force $\backslash ($ F $\backslash ).$

$($a$)$ What is the mechanical advantage of this pulley system? Justify your answer and explain how pulley systems achieve mechanical advantage.

$[4$ marks$]$

$($b$)$ Compute the force $\backslash ($ F $\backslash )$ required to lift the mass $\backslash ($ M $\backslash ).$

$[4$ marks$]$

$($c$)$ Compute the tensile forces in all rope segments $($see numbers $1$ up to $9$ in Figure Q$4).$ What is the sum of forces acting on the ceiling to which the ropes are attached?

$[8$ marks$]$

$($d$)$ If $3$ meters of rope is pulled downwards, as denoted by the direction of the force vector $\backslash ($ F $\backslash ),$ how far did the mass $\backslash ($ M $\backslash )$ move upwards?

$[4$ marks$]$