Problem $5(20$ pts$)$: The system shown consist of two cylindrical masses $(\backslash ($ m$\_\{$A$\}=10\backslash$mathrm$\{$~kg$\},$ m$\_\{$B$\}=8\backslash$mathrm$\{$~kg$\}\backslash ))$ connected by a rope and suspended over a tube that applies a constant pressure. Considering the surface area of mass A $,$ this pressure translates into $\backslash (20-\backslash$mathrm$\{$N$\}\backslash )$ force. The static and kinetic friction coefficient between mass $\backslash ($ A $\backslash )$ and the tube is $0\mathrm{.}6$ ad $0\mathrm{.}5$ respectively. If the system is release from rest in the position shown, determine a$)$ if the system moves and b$)$ if it moves, how far will mass $\backslash ($ A $\backslash )$ compress the spring shown $(\backslash ($ k$=100\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ))$ before it first comes to rest. The bottom of mass $\backslash ($ A $\backslash )$ is initially $\backslash ($ h$=0\mathrm{.}8\backslash$mathrm$\{$~m$\}\backslash )$ above the spring.