### Problem Description:A 100-kg cylinder is hung by means of two cables AB and AC that are attached to the top of a vertical wall. A horizontal force \( P \) perpendicular to the wall holds the cylinder in the position shown. Determine the magnitude of \( P \) and the tension in each cable.### Diagram Explanation:The diagram shows a system in which a 100-kg cylinder is suspended by cables from a wall. The key elements of the diagram are as follows:- **Cylinder:** Located at point \( A \) and labeled as 100 kg.- **Cables AB and AC:** The cables are attached to the wall at points \( B \) and \( C \) and support the cylinder at point \( A \). - Cable \( AB \) is 6 meters long from point \( B \) (on the vertical wall) to point \( A \). - Cable \( AC \) is 5 meters long from point \( C \) (higher on the wall and horizontally distant) to point \( A \).- **Horizontal Force \( P \):** This force acts horizontally to the right from point \( A \).- **Dimensions:** - Horizontal distance from the wall to point \( A \): 0.6 meters. - Vertical distance from cable attachment \( B \) to \( A \): 6 meters. - Horizontal distance from cable attachment \( C \) to \( B \): 4 meters. - Horizontal distance from the wall to the point where \( P \) is applied: 1 meter.### Detailed Explanation:To solve for the magnitude of \( P \) and the tension in each cable, we need to establish the forces in equilibrium. The weight of the cylinder exerts a downward force due to gravity. The tensions in cables AB and AC must counteract this weight and also the horizontal force \( P \). Using principles of static equilibrium (sum of forces in x and y directions equals zero and sum of moments equals zero), we can set up equations to solve for the unknowns.### Mathematical Formulation:Let \( T_{AB} \) be the tension in cable AB, and \( T_{AC} \) be the tension in cable AC.#### 1. Sum of Forces in X-direction:\[ T_{AB} \cdot \sin(\theta_1) + T_{AC} \cdot \sin(\theta_2

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Answered: 5 m 4m |0. 6m 1m 100kg 6 m

Science

Physics

5 m 4m |0. 6m 1m 100kg 6 m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Problem Description:

A 100-kg cylinder is hung by means of two cables AB and AC that are attached to the top of a vertical wall. A horizontal force \( P \) perpendicular to the wall holds the cylinder in the position shown. Determine the magnitude of \( P \) and the tension in each cable.

### Diagram Explanation:

The diagram shows a system in which a 100-kg cylinder is suspended by cables from a wall. The key elements of the diagram are as follows:

- **Cylinder:** Located at point \( A \) and labeled as 100 kg.
- **Cables AB and AC:** The cables are attached to the wall at points \( B \) and \( C \) and support the cylinder at point \( A \).
- Cable \( AB \) is 6 meters long from point \( B \) (on the vertical wall) to point \( A \).
- Cable \( AC \) is 5 meters long from point \( C \) (higher on the wall and horizontally distant) to point \( A \).
- **Horizontal Force \( P \):** This force acts horizontally to the right from point \( A \).
- **Dimensions:**
- Horizontal distance from the wall to point \( A \): 0.6 meters.
- Vertical distance from cable attachment \( B \) to \( A \): 6 meters.
- Horizontal distance from cable attachment \( C \) to \( B \): 4 meters.
- Horizontal distance from the wall to the point where \( P \) is applied: 1 meter.

### Detailed Explanation:

To solve for the magnitude of \( P \) and the tension in each cable, we need to establish the forces in equilibrium. The weight of the cylinder exerts a downward force due to gravity. The tensions in cables AB and AC must counteract this weight and also the horizontal force \( P \). Using principles of static equilibrium (sum of forces in x and y directions equals zero and sum of moments equals zero), we can set up equations to solve for the unknowns.

### Mathematical Formulation:
Let \( T_{AB} \) be the tension in cable AB, and \( T_{AC} \) be the tension in cable AC.

#### 1. Sum of Forces in X-direction:
\[ T_{AB} \cdot \sin(\theta_1) + T_{AC} \cdot \sin(\theta_2

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