A spring AB with $3\mathrm{.}2$ N$/$mm stiffness is attached to a cable at B$.$ The cable wraps around two cylindrical surfaces, and cable segments BC$,$ DE$,$ and GH 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.

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

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The spring constant of spring AB is k$.$ The fixed cylinders have radii of $40$ millimeters and $20$ millimeters. The small cylinder is above the large one. The curved surface of the large cylinder is to the right and the curved surface of the small cylinder is to the left. The cable passes through point C on the bottom section of the large cylinder, point D on the top section of the larger cylinder, point E on the bottom section of the small cylinder, point G on the top section of the small cylinder, and point H to the right of point G$.$ A horizontal vector P from point H is directed to the right. The cable segments BC$,$ DE$,$ and GH are horizontal.

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Once the spring is stretched by $4$ mm$,$ determine the value to which P must be reduced so that the spring begins to contract.$($Round the final answer to four decimal places.$)$

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P must be reduced to N$.$ Required information

A spring $\backslash ($ A B $\backslash )$ with $\backslash (3\mathrm{.}2\backslash$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.

Once the spring is stretched by $4$ mm $,$ determine the value to which $\backslash ($ P $\backslash )$ must be reduced so that the spring begins to contract. $($Round the final answer to four decimal places.$)$

$\backslash ($ P $\backslash )$ must be reduced to

N$.$