$(20\%)$ Problem $1$: A slowly moving conveyor belt passes through a small opening in a wall which is high enough to accommodate a single package, but a reckless worker stacks two packages on the belt. The one at the bottom, package $1$ which has mass $m_1,$ continues, without slipping against the belt, through the opening. $($The belt continues without slowing.$)$ The one on the the top, package $2$ with mass $m_2,$ presses firmly against the wall and slips across the lower package. The same coefficients of friction, ${}_s$ and ${}_k,$ apply between the pair of packages and between the package and the belt.

Weights, if required, will be denoted with the corresponding subscript of the package as vec$(F{)}_{g,i},$ for $i=1,2.$

The normal force exerted by object $a$ on object $b,$ if required, will be denoted as vec$(F{)}_{n,ab}$ for $,$ belt, wall