### Example Problem on Cable Tension and Sag Calculation#### Problem Statement:The cable shown below is supported by two pins at points A and B. The maximum cable tension due to the applied forces is 1000 lb. Determine the tensions in all four segments of the cable and the sags of the load points P1, P2, and P3.#### Diagram:The diagram illustrates a cable suspended between two points, A and B, with the following details:- **Points A and B**: These are fixed support points for the cable.- **Horizontal Distances**: - Distance from A to P1 = 2 feet - Distance from P1 to P2 = 4 feet - Distance from P2 to P3 = 6 feet - Distance from P3 to B = 5 feet- **Vertical Distance**: - Point B is 3 feet higher than point A.- **Loads on the cable**: - A load of 100 lb acts downward at point P1. - A load of 200 lb acts downward at point P2. - A load of 300 lb acts downward at point P3.#### Steps for solution:1. **Calculate Cable Segment Tensions**: - Utilize the principles of static equilibrium and tension to determine the forces in each segment of the cable. - Apply the maximum tension constraint (1000 lb) to solve for the unknowns.2. **Determine Sags at P1, P2, and P3**: - Using geometric relationships and the calculated tensions, find the vertical displacements (sags) of the points P1, P2, and P3.#### Important Equations and Concepts: - **Equilibrium equations** for a cable segment: - Sum of horizontal forces = 0 - Sum of vertical forces = 0- **Geometry and trigonometry principles** to relate linear dimensions to angles and sags.This problem is a classic example in structural engineering and mechanics, aiding in the understanding of tension forces and vertical displacements in cable systems.

Answered: Image /qna-images/answer/ecf817c6-3ff5-45e7-a28c-2399695e9025.jpg

Q.3) The cable shown below is supported by two pins at A and B. The maximum cable tension due to the applied forces is 1000 lb. Determin the tensions in all four segments of the cable and the sags of the load points P1, P2, and P3. B - 5 ft- 3 ft А. 2 ft, 4 ft 6 ft P3 y V 300 Ib

Q.3) The cable shown below is supported by two pins at A and B. The maximum cable tension due to the applied forces is 1000 lb. Determin the tensions in all four segments of the cable and the sags of the load points P1, P2, and P3. B - 5 ft- 3 ft А. 2 ft, 4 ft 6 ft P3 y V 300 Ib

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

### Example Problem on Cable Tension and Sag Calculation

#### Problem Statement:

The cable shown below is supported by two pins at points A and B. The maximum cable tension due to the applied forces is 1000 lb. Determine the tensions in all four segments of the cable and the sags of the load points P1, P2, and P3.

#### Diagram:

The diagram illustrates a cable suspended between two points, A and B, with the following details:

- **Points A and B**: These are fixed support points for the cable.
- **Horizontal Distances**:
- Distance from A to P1 = 2 feet
- Distance from P1 to P2 = 4 feet
- Distance from P2 to P3 = 6 feet
- Distance from P3 to B = 5 feet
- **Vertical Distance**:
- Point B is 3 feet higher than point A.
- **Loads on the cable**:
- A load of 100 lb acts downward at point P1.
- A load of 200 lb acts downward at point P2.
- A load of 300 lb acts downward at point P3.

#### Steps for solution:

1. **Calculate Cable Segment Tensions**:
- Utilize the principles of static equilibrium and tension to determine the forces in each segment of the cable.
- Apply the maximum tension constraint (1000 lb) to solve for the unknowns.

2. **Determine Sags at P1, P2, and P3**:
- Using geometric relationships and the calculated tensions, find the vertical displacements (sags) of the points P1, P2, and P3.

#### Important Equations and Concepts:

- **Equilibrium equations** for a cable segment:
- Sum of horizontal forces = 0
- Sum of vertical forces = 0
- **Geometry and trigonometry principles** to relate linear dimensions to angles and sags.

This problem is a classic example in structural engineering and mechanics, aiding in the understanding of tension forces and vertical displacements in cable systems.

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