5-2. The cable supports the loading shown. Determine the magnitude of the vertical force P so that yo = 10 ft. Prob. 5-2 -4 ft- 10 ft- 8 ft 5 ft B P 4 k D Ус

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Question
### Problem 5–2: Cable Support Analysis

The diagram illustrates a cable supporting two vertical loads. The task is to determine the magnitude of vertical force \( P \) such that \( y_C = 10 \, \text{ft} \).

#### Diagram Details:

- **Supports**:
  - Point \( A \) and \( D \) are the cable's supports on the horizontal surface.
  - The distance from the horizontal surface to point \( A \): \( 5 \, \text{ft} \).
  - The vertical distance from the horizontal surface to point \( D \) is labeled \( y_C \).

- **Distances**:
  - Horizontal distance between point \( A \) and support of cable: \( 4 \, \text{ft} \).
  - Horizontal distance from point \( A \) to point \( C \) is \( 10 \, \text{ft} \).
  - Horizontal distance from point \( C \) to point \( D \) is \( 8 \, \text{ft} \).

- **Forces**:
  - At point \( B \), directly below point \( A \), there is an unknown vertical force \( P \).
  - At point \( C \), located between \( B \) and \( D \), there is a vertical force of \( 4 \, \text{kip} \) (4,000 lb).

### Objective:

The challenge is to calculate the force \( P \) such that point \( C \) remains \( 10 \, \text{ft} \) below the horizontal.
  
Use principles of static equilibrium and geometry to solve for \( P \). Consider tension in the cable and analyze forces vertically and horizontally for equilibrium.
Transcribed Image Text:### Problem 5–2: Cable Support Analysis The diagram illustrates a cable supporting two vertical loads. The task is to determine the magnitude of vertical force \( P \) such that \( y_C = 10 \, \text{ft} \). #### Diagram Details: - **Supports**: - Point \( A \) and \( D \) are the cable's supports on the horizontal surface. - The distance from the horizontal surface to point \( A \): \( 5 \, \text{ft} \). - The vertical distance from the horizontal surface to point \( D \) is labeled \( y_C \). - **Distances**: - Horizontal distance between point \( A \) and support of cable: \( 4 \, \text{ft} \). - Horizontal distance from point \( A \) to point \( C \) is \( 10 \, \text{ft} \). - Horizontal distance from point \( C \) to point \( D \) is \( 8 \, \text{ft} \). - **Forces**: - At point \( B \), directly below point \( A \), there is an unknown vertical force \( P \). - At point \( C \), located between \( B \) and \( D \), there is a vertical force of \( 4 \, \text{kip} \) (4,000 lb). ### Objective: The challenge is to calculate the force \( P \) such that point \( C \) remains \( 10 \, \text{ft} \) below the horizontal. Use principles of static equilibrium and geometry to solve for \( P \). Consider tension in the cable and analyze forces vertically and horizontally for equilibrium.
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