Beam $\backslash ($ A B $\backslash )$ has a negligible mass and thickness, and supports the $200-$kg uniform block as shown in $($Figure $1).$ It is pinned at $\backslash ($ A $\backslash )$ and rests on the top of a post, having a mass of $20$ kg and negligible thickness.

Figure

Part A

Determine the two coefficients of static friction at $\backslash ($ B $\backslash )$ and at $\backslash ($ C $\backslash )$ so that when the magnitude of the applied force is increased to $450$ N $,$ the post slips at both $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash )$ simultaneously.

Express your answers using three significant figures separated by a comma.

$\backslash [$

$\backslash$mu$\_\{$B$\},\backslash$mu$\_\{$C$\}=\backslash$square

$\backslash ]$