Problem points$)$:

In the mechanism shown to the right, a cable attached

to spring $1($stiffness of $4l\frac{b}{i}n,$ undeformed length of $20$

inches$)$ wraps around two pulleys. One of the pulleys

is pinned to a collar at point A and the other pulley is

pinned to a wall at $D.$ The cable is being pulled straight

up with a force P of $25$ lb at its free end. The collar at

A slides without friction on bar CE along the vertical

direction, without rotation. There is a spring around the

segment AC $($stiffness of $5l\frac{b}{i}n$ and deformed length of

$15$ inches$)$ of the bar that is attached to both the collar

and the ceiling. Ignore the size of the collar and of the

pulleys in your analysis. Assuming that the mechanism

is in static equilibrium:

$($a$)$ Find the final length of spring $1.$

$($b$)$ Find the undeformed length of spring $2.$

$($c$)$ Find the reaction force$($s$)$ on the collar.