Two boxes $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ are connected via a massless, inextensible vertical rope $($see the diagram$).$ The system is held still and is initially at rest. At time $\backslash ($ t$\_\{1\}\backslash ),$ the system is released, and box $\backslash ($ A $\backslash )$ is now acted upon by an upward vertical constant force $\backslash ($ F$=50\backslash$mathrm$\{$~N$\}\backslash ),$ while box $\backslash ($ B $\backslash )$ moves $24$ m downward in $4$ s $.$ The tension $\backslash ($ T $\backslash )$ in the rope between the two boxes is $23$ N $.$

Determine the mass $\backslash ($ m$\_\{$A$\}\backslash )$ of box $\backslash ($ A $\backslash )$ :