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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![### Example Problem on Statics: Tension in Cables
**Problem Statement:**
A 50 kg cylinder is hanging by the cables from the ceiling. Determine the magnitude of tensions in cables AB, AC, and AD. You must solve this problem using statics methods. Assume the value of \( g \) is 9.80 \(\text{m/s}^2\).
**Diagram Explanation:**
The diagram shows a 3D coordinate system with four points: A, B, C, and D.
- Point \( A \) is at coordinates \( (0, -4, 0) \) m. This is the point from which the cylinder is hanging.
- Point \( B \) is at coordinates \( (4, 0, 1) \) m. This is the fixed point where cable AB is attached to the ceiling.
- Point \( C \) is at coordinates \( (-2, 0, -2) \) m. This is the fixed point where cable AC is attached to the ceiling.
- Point \( D \) is at coordinates \( (-3, 0, 3) \) m. This is the fixed point where cable AD is attached to the ceiling.
The cylinder hanging from point \( A \) has a mass of 50 kg. The forces acting on the cylinder due to the cables \( AB, AC, \) and \( AD \) will be determined using static equilibrium conditions.
### Steps to Solve:
1. **Calculate the weight of the cylinder:**
\[
\text{Weight} (W) = m \cdot g = 50 \, \text{kg} \cdot 9.80 \, \text{m/s}^2 = 490 \, \text{N}
\]
This weight acts downward at point \( A \).
2. **Set up equilibrium equations:**
For static equilibrium, the sum of forces in the \( x\)-, \( y\)-, and \( z\)-directions must be zero. Thus, we have:
- \( \sum F_x = 0 \)
- \( \sum F_y = 0 \)
- \( \sum F_z = 0 \)
3. **Express tensions in the cables as vectors:**
- \( \vec{T}_{AB} = T_{AB} \left( \frac{\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e4fcbe0-ed74-4447-b38a-a2af13f9fabc%2F75480224-c93c-447b-83d2-66979e33f49a%2F7ezmoqb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem on Statics: Tension in Cables
**Problem Statement:**
A 50 kg cylinder is hanging by the cables from the ceiling. Determine the magnitude of tensions in cables AB, AC, and AD. You must solve this problem using statics methods. Assume the value of \( g \) is 9.80 \(\text{m/s}^2\).
**Diagram Explanation:**
The diagram shows a 3D coordinate system with four points: A, B, C, and D.
- Point \( A \) is at coordinates \( (0, -4, 0) \) m. This is the point from which the cylinder is hanging.
- Point \( B \) is at coordinates \( (4, 0, 1) \) m. This is the fixed point where cable AB is attached to the ceiling.
- Point \( C \) is at coordinates \( (-2, 0, -2) \) m. This is the fixed point where cable AC is attached to the ceiling.
- Point \( D \) is at coordinates \( (-3, 0, 3) \) m. This is the fixed point where cable AD is attached to the ceiling.
The cylinder hanging from point \( A \) has a mass of 50 kg. The forces acting on the cylinder due to the cables \( AB, AC, \) and \( AD \) will be determined using static equilibrium conditions.
### Steps to Solve:
1. **Calculate the weight of the cylinder:**
\[
\text{Weight} (W) = m \cdot g = 50 \, \text{kg} \cdot 9.80 \, \text{m/s}^2 = 490 \, \text{N}
\]
This weight acts downward at point \( A \).
2. **Set up equilibrium equations:**
For static equilibrium, the sum of forces in the \( x\)-, \( y\)-, and \( z\)-directions must be zero. Thus, we have:
- \( \sum F_x = 0 \)
- \( \sum F_y = 0 \)
- \( \sum F_z = 0 \)
3. **Express tensions in the cables as vectors:**
- \( \vec{T}_{AB} = T_{AB} \left( \frac{\
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