A cable and a spring are connected together at point B and held in equilibrium by a vertical force $F,$ as

shown in the figure below. The cable has a length $L_{AB}=1ft$ and is oriented at an angle $=30$ from the

horizontal, and the spring has a spring constant $k=70l\frac{b}{f}t.$ Note that the cable and unstretched spring

were initially aligned horizontally between points A and C before loading, with a combined length of

$L_w=3ft.$ Determine the force in the spring $(F_{BC})$ and the applied force $F.$

$[F_{BC}=,lb?],[F=$ humber $($ rtol $=0\mathrm{.}01,$ atol Two weights $W_B$ and $W_C$ are supported by three cables $(AB,BC,$ and CD $),$ as shown in the figure below.

The vertical distances between points $A$&$B,B$&$C,$ and $C$&$D$ are given by $h_{AB}=7\mathrm{.}5m,h_{BC}=2\mathrm{.}5m,$

and $h_{CD}=9m$ respectively. If $W_B=110N,$ determine the forces in all three cables and the weight $W_C.$