Let's solve the problem step by step. --- # **Given:** - Weight at C, \( W = 50\, \text{kg} \) - Gravitational acceleration, \( g = 9.81\, \text{m/s}^2 \) - Weight force, \( F_W = W \cdot g = 50 \cdot 9.81 = 490.5\, \text{N} \) - Find tension in cable \( AC \) (\( T_{AC} \)) and in cable \( BC \) (\( T_{BC} \)) ## **1. Draw the Free Body Diagram at C** ### Forces acting at C: - Tension \( T_{AC} \) along \( AC \) (20° above horizontal) - Tension \( T_{BC} \) along \( BC \) (20° below horizontal) - Weight downwards \( W = 490.5\, \text{N} \) --- ## **2. Resolve Forces into Components** Assume: - \( T_{AC} \) makes a 20° angle above the horizontal (to the right) - \( T_{BC} \) makes a 20° angle below the horizontal (to the left) Let’s take right as positive \( x \), up as positive \( y \): ### **Tension \( T_{AC} \):** - \( T_{AC,x} = T_{AC} \cos 20^\circ \) - \( T_{AC,y} = T_{AC} \sin 20^\circ \) ### **Tension \( T_{BC} \):** - \( T_{BC,x} = -T_{BC} \cos 20^\circ \) (since it's to the left) - \( T_{BC,y} = T_{BC} \sin 20^\circ \) (since it's up) ### **Weight:** - \( F_{W,x} = \) - \( F_{W,y} = -490.5\, \text{N} \) --- ## **3. Apply Equilibrium Equations at Point C** ### **Horizontal (\( x \)) direction:** \[ T_{AC} \cos 20^\circ - T_{BC} \cos 20^\circ = \] \[ T_{AC} \cos 20^\circ = T_{BC} \cos 20^\circ \] \[ T_{AC} = T_{BC} \] ### **Vertical (\( y \)) direction:** \[ T_{AC} \sin 20^\circ + T_{BC} \sin 20^\circ - 490.5 = \] Since \( T_{AC} = T_{BC} \): \[ 2 T_{AC} \sin 20^\circ = 490.5 \] \[ T_{AC} = \frac{490.5}{2 \sin 20^\circ} \] --- ## **4. Calculate the Tension** \[ \sin 20^\circ \approx .342 \] \[ T_{AC} = \frac{490.5}{2 \times .342} \] \[ T_{AC} = \frac{490.5}{.684} \] \[ T_{AC} \approx 717.5\, \text{N} \] Since \( T_{AC} = T_{BC} \): \[ T_{BC} \approx 717.5\, \text{N} \] --- ## **5. Final Answers** ### **Tension in cable AC:** \[ \boxed{717.5\, \text{N}} \] ### **Tension in cable BC:** \[ \boxed{717.5\, \text{N}} \] --- ### **Summary Table** | Cable | Tension (N) | |---------|-------------| | AC | 717.5 | | BC | 717.5 | --- **If you need a diagram or further explanation, let me know!**