Problem $08\mathrm{.}020-$ Force required to draw wire from a spool

Wire is being drawn at a constant rate from a spool by applying a vertical force $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ to the wire as shown. The spool and the wire wrapped on the spool have a combined weight of $19$ lb $.$ Knowing that the coefficients of friction at $\backslash ($ A $\backslash )$ are $\backslash (\backslash$mu$\_\{$s$\}=0\mathrm{.}40\backslash )$ and $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}30\backslash )$ and zero at $\backslash ($ B $\backslash ),$ determine the required magnitude of the force $\backslash (\backslash$mathbf$\{$P$\}\backslash ).$

The required magnitude of the force $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ is $9\mathrm{.}5$ lb $.$