1. The 6-m boom AB has a fixed end at A. A steel cable is stretched from the free end B of the boom to point C located on the vertical wall. If the tension in the cable is 2.5 kN, determine the moment about A due to the force exerted by the cable at B. Ans: M=0f +7.89 j+4.74k kN m 4 m 2.4 m A 6 m xr
1. The 6-m boom AB has a fixed end at A. A steel cable is stretched from the free end B of the boom to point C located on the vertical wall. If the tension in the cable is 2.5 kN, determine the moment about A due to the force exerted by the cable at B. Ans: M=0f +7.89 j+4.74k kN m 4 m 2.4 m A 6 m xr
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 Statement:**
1. The 6-m boom \(AB\) has a fixed end at \(A\). A steel cable is stretched from the free end \(B\) of the boom to point \(C\) located on the vertical wall. If the tension in the cable is 2.5 kN, determine the moment about \(A\) due to the force exerted by the cable at \(B\).
**Solution:**
The answer for the moment \(\vec{M}_A\) about point \(A\) is given by:
\[
\vec{M}_A = 0\hat{i} + 7.89\hat{j} + 4.74\hat{k} \text{ kN} \cdot \text{m}
\]
**Diagram Explanation:**
- The diagram shows a three-dimensional view of the setup.
- The boom \(AB\) is 6 meters long and extends along the x-axis from point \(A\).
- Point \(C\) is located on the vertical wall 4 meters along the y-axis and 2.4 meters along the z-axis.
- The steel cable is drawn tightly from point \(B\) at the boom's free end to point \(C\), forming a diagonal in the y-z plane.
This kind of problem is common in engineering mechanics, particularly when analyzing structures subjected to forces, as it involves determining moments and understanding the spatial relationships between different components.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c92bfa8-de7b-4872-bcff-5b3a3db686c0%2F4622824e-b591-43ee-a785-26672bef2de9%2F2wdbcc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
1. The 6-m boom \(AB\) has a fixed end at \(A\). A steel cable is stretched from the free end \(B\) of the boom to point \(C\) located on the vertical wall. If the tension in the cable is 2.5 kN, determine the moment about \(A\) due to the force exerted by the cable at \(B\).
**Solution:**
The answer for the moment \(\vec{M}_A\) about point \(A\) is given by:
\[
\vec{M}_A = 0\hat{i} + 7.89\hat{j} + 4.74\hat{k} \text{ kN} \cdot \text{m}
\]
**Diagram Explanation:**
- The diagram shows a three-dimensional view of the setup.
- The boom \(AB\) is 6 meters long and extends along the x-axis from point \(A\).
- Point \(C\) is located on the vertical wall 4 meters along the y-axis and 2.4 meters along the z-axis.
- The steel cable is drawn tightly from point \(B\) at the boom's free end to point \(C\), forming a diagonal in the y-z plane.
This kind of problem is common in engineering mechanics, particularly when analyzing structures subjected to forces, as it involves determining moments and understanding the spatial relationships between different components.
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