Do not round intermediate answers. Give your final answer$($s$)$ to three decimal places. Check your units.

A cable passes around three $3-$in$.-$radius pulleys and supports two blocks as shown. Pulleys $\backslash ($ C $\backslash )$ and $\backslash ($ E $\backslash )$ are locked to prevent rotation, and the coefficients of friction between the cable and the pulleys are $\backslash (\backslash$mu$\_\{$s$\}=0\mathrm{.}28\backslash )$ and $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}21\backslash ).$ Determine the value of the weight of block $\backslash ($ A $\backslash )$ for which equilibrium is maintained if it were to impend upward and:

$($a$)$ if pulley $\backslash ($ D $\backslash )$ is locked,

$($b$)$ if pulley $\backslash ($ D $\backslash )$ is free to rotate.

$($a$)$ W of $\backslash (\backslash$mathrm$\{$A$\}=\backslash )$ lbs

$($b$)$ W of $\backslash (\backslash$mathrm$\{$A$\}=\backslash )$ lbs