1. When the plastic bushing shown to the right is inserted into a cylindrical enclosure, the insertion tools exert the forces shown in the figure to the right. The diameter of the bushing (cylinder) is 60 mm. Each of the forces is parallel to one of the coordinate axes. Find the resultant force and the resultant moment at point C. Ř=-2lî - 29j–16k N %3D Ans.: M =-0.87î +0.63ĵ+0.39k N - m C
1. When the plastic bushing shown to the right is inserted into a cylindrical enclosure, the insertion tools exert the forces shown in the figure to the right. The diameter of the bushing (cylinder) is 60 mm. Each of the forces is parallel to one of the coordinate axes. Find the resultant force and the resultant moment at point C. Ř=-2lî - 29j–16k N %3D Ans.: M =-0.87î +0.63ĵ+0.39k N - m C
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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![**Problem Analysis and Solution Explanation**
**Problem Statement:**
When the plastic bushing (cylinder) with a diameter of 60 mm is inserted into a cylindrical enclosure, it experiences forces as depicted in the diagram. Each force is aligned with one of the coordinate axes. The task is to determine the resultant force and the resultant moment at point \( C \).
**Given Data:**
- Diameter of the bushing: 60 mm
**Forces Acting on the Cylinder:**
- Force \( \vec{A} = 17 \, \text{N} \) (acts along the negative \( y \)-axis)
- Force \( \vec{B} = 12 \, \text{N} \) (acts along the negative \( z \)-axis)
- Force \( \vec{D} = 21 \, \text{N} \) (acts along the negative \( x \)-axis)
- Force \( \vec{C} = 16 \, \text{N} \) (acts along the positive \( z \)-axis)
**Distances:**
- Distance from line of action of \( \vec{A} \) to the \( z \)-axis: 20 mm
- Vertical distance from line of action of \( \vec{B} \) to point \( C \): 140 mm (80 mm + 60 mm)
- Distance from \( \vec{C} \) to the \( z \)-axis: 30 mm
**Resultant Force and Moment Calculation:**
- **Resultant Force \( \vec{R} \):**
\[
\vec{R} = -21\hat{i} - 29\hat{j} - 16\hat{k} \, \text{N}
\]
- **Resultant Moment at Point \( C \), \( \vec{M}_C \):**
\[
\vec{M}_C = -0.87\hat{i} + 0.63\hat{j} + 0.39\hat{k} \, \text{N} \cdot \text{m}
\]
**Diagram Explanation:**
The diagram shows a cylindrical bushing oriented vertically. Several forces are applied:
- \( \vec{A} \) and \( \vec{B} \) are applied at the top face of the cylinder.
- \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c92bfa8-de7b-4872-bcff-5b3a3db686c0%2F12593b5b-db1f-498d-ad00-d54b39ae9b7e%2Fp4inj4l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Analysis and Solution Explanation**
**Problem Statement:**
When the plastic bushing (cylinder) with a diameter of 60 mm is inserted into a cylindrical enclosure, it experiences forces as depicted in the diagram. Each force is aligned with one of the coordinate axes. The task is to determine the resultant force and the resultant moment at point \( C \).
**Given Data:**
- Diameter of the bushing: 60 mm
**Forces Acting on the Cylinder:**
- Force \( \vec{A} = 17 \, \text{N} \) (acts along the negative \( y \)-axis)
- Force \( \vec{B} = 12 \, \text{N} \) (acts along the negative \( z \)-axis)
- Force \( \vec{D} = 21 \, \text{N} \) (acts along the negative \( x \)-axis)
- Force \( \vec{C} = 16 \, \text{N} \) (acts along the positive \( z \)-axis)
**Distances:**
- Distance from line of action of \( \vec{A} \) to the \( z \)-axis: 20 mm
- Vertical distance from line of action of \( \vec{B} \) to point \( C \): 140 mm (80 mm + 60 mm)
- Distance from \( \vec{C} \) to the \( z \)-axis: 30 mm
**Resultant Force and Moment Calculation:**
- **Resultant Force \( \vec{R} \):**
\[
\vec{R} = -21\hat{i} - 29\hat{j} - 16\hat{k} \, \text{N}
\]
- **Resultant Moment at Point \( C \), \( \vec{M}_C \):**
\[
\vec{M}_C = -0.87\hat{i} + 0.63\hat{j} + 0.39\hat{k} \, \text{N} \cdot \text{m}
\]
**Diagram Explanation:**
The diagram shows a cylindrical bushing oriented vertically. Several forces are applied:
- \( \vec{A} \) and \( \vec{B} \) are applied at the top face of the cylinder.
- \(
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