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A bent tube is attached to a wall with brackets as shown. . A force of F = 670 lb is applied to the end of the tube with direction indicated by the dimensions in the figure. a.) Determine the force vector F in Cartesian components. b.) Resolve the force vector F into vector components parallel and perpendicular to the position vector TDA. Express each of these vectors in Cartesian components.

A bent tube is attached to a wall with brackets as shown. . A force of F = 670 lb is applied to the end of the tube with direction indicated by the dimensions in the figure. a.) Determine the force vector F in Cartesian components. b.) Resolve the force vector F into vector components parallel and perpendicular to the position vector TDA. Express each of these vectors in Cartesian components.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**Transcription for Educational Website** --- A bent tube is attached to a wall with brackets as shown. A force of \( F = 670 \) lb is applied to the end of the tube with directions indicated by the dimensions in the figure. **a.)** Determine the force vector \(\vec{F}\) in Cartesian components. **b.)** Resolve the force vector \(\vec{F}\) into vector components parallel and perpendicular to the position vector \(\vec{r}_{DA}\). Express each of these vectors in Cartesian components. **Diagram Description:** The diagram depicts a bent tube structure attached to a wall with brackets. The tube segments are labeled as follows: - \( A \), \( B \), \( C \), and \( D \) represent key points. - The dimensions for the tube's position relative to the wall are marked: \( x \), \( y \), and \( z \) axes. The specific directions are given as: - \( a \), \( b \), \( c \), \( d \), \( g \), \( h \) An arrow at point \( A \) indicates the force vector \( F \) acting diagonally relative to the \( x \), \( y \), and \( z \) axes. **Values for dimensions are given in a table (not visible in image).** Note the figure may not be to scale. The coordinate axes are shown for aligning Cartesian unit vectors. --- Copyright © 2013 Michael Swanbom Creative Commons License: BY-NC-SA (Note: Exact values for dimensions should be referenced from accompanying table data in resources.)
Transcribed Image Text:**Transcription for Educational Website** --- A bent tube is attached to a wall with brackets as shown. A force of \( F = 670 \) lb is applied to the end of the tube with directions indicated by the dimensions in the figure. **a.)** Determine the force vector \(\vec{F}\) in Cartesian components. **b.)** Resolve the force vector \(\vec{F}\) into vector components parallel and perpendicular to the position vector \(\vec{r}_{DA}\). Express each of these vectors in Cartesian components. **Diagram Description:** The diagram depicts a bent tube structure attached to a wall with brackets. The tube segments are labeled as follows: - \( A \), \( B \), \( C \), and \( D \) represent key points. - The dimensions for the tube's position relative to the wall are marked: \( x \), \( y \), and \( z \) axes. The specific directions are given as: - \( a \), \( b \), \( c \), \( d \), \( g \), \( h \) An arrow at point \( A \) indicates the force vector \( F \) acting diagonally relative to the \( x \), \( y \), and \( z \) axes. **Values for dimensions are given in a table (not visible in image).** Note the figure may not be to scale. The coordinate axes are shown for aligning Cartesian unit vectors. --- Copyright © 2013 Michael Swanbom Creative Commons License: BY-NC-SA (Note: Exact values for dimensions should be referenced from accompanying table data in resources.)
**Figure Explanation:** The diagram shows a rectangular shape with dimensions labeled as \(a\) and \(b\) along the x-axis and y-axis respectively. **Values for Dimensions:** - **Note:** The figure may not be to scale. Align your Cartesian unit vectors with the coordinate axes shown in the figure. **Table of Dimensions:** | Variable | Value | |----------|-------| | \( a \) | 7 in | | \( b \) | 19 in | | \( c \) | 14 in | | \( d \) | 53 in | | \( h \) | 36 in | | \( g \) | 38 in | **Vector Calculations:** a. \(\vec{F} = \begin{pmatrix} 618 \\ -228 \\ -455 \end{pmatrix} \text{lb}\) - The vector \(\vec{F}\) has components: - \(618 \, \hat{i}\) - \(-228 \, \hat{j}\) - \(-455 \, \hat{k}\) b. \(\vec{F}_{\parallel DA} = \begin{pmatrix} \ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{pmatrix} \text{lb and} \ \ \vec{F}_{\perp DA} = \begin{pmatrix} \ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{pmatrix} \text{lb}\) - Placeholder for parallel and perpendicular components to line DA, with empty components to be filled out.
Transcribed Image Text:**Figure Explanation:** The diagram shows a rectangular shape with dimensions labeled as \(a\) and \(b\) along the x-axis and y-axis respectively. **Values for Dimensions:** - **Note:** The figure may not be to scale. Align your Cartesian unit vectors with the coordinate axes shown in the figure. **Table of Dimensions:** | Variable | Value | |----------|-------| | \( a \) | 7 in | | \( b \) | 19 in | | \( c \) | 14 in | | \( d \) | 53 in | | \( h \) | 36 in | | \( g \) | 38 in | **Vector Calculations:** a. \(\vec{F} = \begin{pmatrix} 618 \\ -228 \\ -455 \end{pmatrix} \text{lb}\) - The vector \(\vec{F}\) has components: - \(618 \, \hat{i}\) - \(-228 \, \hat{j}\) - \(-455 \, \hat{k}\) b. \(\vec{F}_{\parallel DA} = \begin{pmatrix} \ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{pmatrix} \text{lb and} \ \ \vec{F}_{\perp DA} = \begin{pmatrix} \ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{pmatrix} \text{lb}\) - Placeholder for parallel and perpendicular components to line DA, with empty components to be filled out.
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