Problem $4(10$ pts$)$

Consider Fig. $4$ and assume $W$ is known. The rope attached to the wall is guided without friction through $K.$ You can think of it as a frictionless pulley.

$($a$)$ Draw the free$-$body diagram at point $K.($Note there are more than four forces$).(3$ pts$)$

$($b$)$ Express all the forces as vectors in the reference frame $E\{hat(e{)}_1,$hat$(e{)}_2,$hat$(e{)}_3\}.(4$ pts$)$

$($c$)$ Find the magnitude of the forces in the bars and state whether they are working in tension or compression. $(3$ pts$)$