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This is a statics problem involving a pulley and a continuous cable system. The container weighing \( W = 300 \, \text{lb} \) is suspended from point \( A \), with a cable running from \( B \) to \( A \) to \( C \). The system can be analyzed using principles of equilibrium and geometry.

From the diagram, we know:

- The distance between the two walls is \( L_w = 45 \, \text{ft} \).
- The vertical sag between the two supports is \( h = 6 \, \text{ft} \).
- The total length of the cable \( L_{BAC} = 50 \, \text{ft} \).
- The angles of the cable at both supports \( B \) and \( C \) with respect to the horizontal are denoted as \( \theta \).
  
The following unknowns must be determined:
1. The angle \( \theta \) that the cable makes with the horizontal.
2. The horizontal and vertical distances: \( h_{BA} \), \( h_{AC} \), and \( x \).
3. The tensions in the cable segments \( BA \) and \( AC \).

### Approach to Solution:

1. **Geometry of the System:**
   - Define \( x \) as the horizontal distance from \( A \) to the right wall.
   - The total length of the cable is \( L_{BAC} \), so we can use geometric constraints and trigonometric relations to express the length of the segments \( BA \) and \( AC \).

2. **Equilibrium Conditions:**
   - For equilibrium, the sum of forces in both the horizontal and vertical directions must be zero. This provides equations for the tensions in the cable and the angle \( \theta \).

Would you like me to solve this problem step by step starting with the geometric constraints, or is there a particular part of the problem you'd like to focus on first?

A container of weight W = 300 lb is supported by a continuous cable BAC and a small pulley at A. The cable is attached between two walls that are Lw = 45 ft apart, and the right support at C is h = 6 ft below the left support at B. Cable BAC has a total length LBAC = 50 ft and sags prior to adding the pulley and container. From equilibrium considerations, we can prove that cable segments BA and AC are inclined at the same angle θ from the horizontal. Neglect the size and weight of the pulley for this analysis. Determine the following quantities: angle θ, horizontal and vertical distances (hBA, hAC, x), and the tensions in cable segments BA and AC.

Analyze a statics pulley problem where a 300 lb container is supported by a continuous cable between two walls 45 ft apart. Determine the angle of inclination, horizontal and vertical distances, and tensions in the cable. Learn how to apply force equilibrium and geometry principles for a detailed solution.

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