ft$-$lb The $23-$ lb collar $\backslash ($ A $\backslash )$ is released from rest in the position shown and slides with negligible friction up the fixed rod inclined $\backslash (28^\{\backslash$circ$\}\backslash )$ from the horizontal under the action of a constant force $\backslash ($ P$=39\backslash$mathrm$\{$lb$\}\backslash )$ applied to the cable. Calculate the required stiffness $\backslash ($ k $\backslash )$ of the spring so that its maximum deflection equals $8$ in $.$ The position of the small pulley at $\backslash ($ B $\backslash )$ is fixed.

Answer: $\backslash ($ k$=\backslash )\backslash (\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}\backslash )$