Required information

A spring $\backslash ($ A B $\backslash )$ with $\backslash (4\mathrm{.}8\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}\backslash )$ stiffness is attached to a cable at $\backslash ($ B $\backslash ).$ The cable wraps around two cylindrical surfaces, and cable segments $\backslash ($ B C$,$ D E $\backslash ),$ and $\backslash ($ G H $\backslash )$ are horizontal. All contact surfaces have coefficients of static and kinetic friction of $0\mathrm{.}1$ and $0\mathrm{.}09,$ respectively. The spring is initially unstretched.

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Determine the value of $\backslash ($ P $\backslash )$ needed to stretch the spring by $4$ mm $.($Round the final answer to four decimal places.$)$

The value of $\backslash ($ P $\backslash )$ needed is

N$.$