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The three forces act on the pipe assembly. If F1 = 50 N and F2 = 80 N, replace this force system by an equivalent resultant force and couple moment acting at O. Express the result in Cartesian vector form. Solution R = -210 k, M = -15 i+ 225 j %3D

The three forces act on the pipe assembly. If F1 = 50 N and F2 = 80 N, replace this force system by an equivalent resultant force and couple moment acting at O. Express the result in Cartesian vector form. Solution R = -210 k, M = -15 i+ 225 j %3D

Elements Of Electromagnetics
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:** The three forces act on the pipe assembly. If \( F_1 = 50 \, \text{N} \) and \( F_2 = 80 \, \text{N} \), replace this force system by an equivalent resultant force and couple moment acting at \( O \). Express the result in Cartesian vector form. Solution \( R = -210 \, \mathbf{k} \), \( M = -15 \, \mathbf{i} + 225 \, \mathbf{j} \). **Diagram Explanation:** The diagram shows a pipe assembly in a 3D coordinate system with axes labeled \( x \), \( y \), and \( z \). The assembly consists of pipes connected at right angles, with three forces acting on the system: 1. A 180 N force acting vertically along the \( z \)-axis at point \( O \). 2. \( F_1 = 50 \, \text{N} \) acting vertically upward along an extension parallel to the \( y \)-axis. The location for this force is 0.5 m along the \( y \)-axis from point \( O \). 3. \( F_2 = 80 \, \text{N} \) acting vertically downward, located 0.75 m along the \( y \)-axis from the point of \( F_1 \). Distances from point \( O \) to the locations of \( F_1 \) and \( F_2 \) are marked on the diagram as 0.5 m and 0.75 m, respectively, along the \( y \)-axis, and 1.25 m on the \( z \)-axis from the pipe connection. **Solution:** The equivalent resultant force \( R \) at point \( O \) is given by \( -210 \, \mathbf{k} \). The couple moment \( M \) acting at point \( O \) is expressed as \( -15 \, \mathbf{i} + 225 \, \mathbf{j} \). This setup involves calculating the resultant force and moment using vector principles to replace the original forces. The Cartesian vector form provides a mathematical representation of these equivalent forces and moments in the \( x \), \( y \), and \( z \) directions.
Transcribed Image Text:**Problem Statement:** The three forces act on the pipe assembly. If \( F_1 = 50 \, \text{N} \) and \( F_2 = 80 \, \text{N} \), replace this force system by an equivalent resultant force and couple moment acting at \( O \). Express the result in Cartesian vector form. Solution \( R = -210 \, \mathbf{k} \), \( M = -15 \, \mathbf{i} + 225 \, \mathbf{j} \). **Diagram Explanation:** The diagram shows a pipe assembly in a 3D coordinate system with axes labeled \( x \), \( y \), and \( z \). The assembly consists of pipes connected at right angles, with three forces acting on the system: 1. A 180 N force acting vertically along the \( z \)-axis at point \( O \). 2. \( F_1 = 50 \, \text{N} \) acting vertically upward along an extension parallel to the \( y \)-axis. The location for this force is 0.5 m along the \( y \)-axis from point \( O \). 3. \( F_2 = 80 \, \text{N} \) acting vertically downward, located 0.75 m along the \( y \)-axis from the point of \( F_1 \). Distances from point \( O \) to the locations of \( F_1 \) and \( F_2 \) are marked on the diagram as 0.5 m and 0.75 m, respectively, along the \( y \)-axis, and 1.25 m on the \( z \)-axis from the pipe connection. **Solution:** The equivalent resultant force \( R \) at point \( O \) is given by \( -210 \, \mathbf{k} \). The couple moment \( M \) acting at point \( O \) is expressed as \( -15 \, \mathbf{i} + 225 \, \mathbf{j} \). This setup involves calculating the resultant force and moment using vector principles to replace the original forces. The Cartesian vector form provides a mathematical representation of these equivalent forces and moments in the \( x \), \( y \), and \( z \) directions.
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