Calculate A) the moment of force about point O and B) the moment of force about point A given that the applied force is F = 450i - 150j - 350k. 1.5 ft 0.25 ft 8 ft

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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3.) please help calculate the moments
The image depicts a 3D diagram of a structural beam. The beam is placed in an XYZ coordinate system and is aligned along the Y-axis. 

Key points and dimensions in the diagram:

- **O** is the origin point at one end of the beam. The coordinates are aligned such that the Y-axis runs along the length of the beam.
  
- **A** and **B** are labeled points on the beam:
  - **A** is at the top right corner of the front face.
  - **B** is at the bottom of the front face, where a force **F** is applied.

- **F** represents a force acting perpendicular to the surface at point **B**. The arrow indicates the direction of the force application.

- The length of the beam along the Y-axis is labeled as **8 ft**.

- The vertical distance from the point **B** to the top of the beam is **1.5 ft**.

- The horizontal distance from point **O** to the edge of the beam along the X-axis is **0.25 ft**.

This diagram is often used in structural engineering to analyze the effects of forces applied at specific points on a beam, helping in stress and load distribution calculations.
Transcribed Image Text:The image depicts a 3D diagram of a structural beam. The beam is placed in an XYZ coordinate system and is aligned along the Y-axis. Key points and dimensions in the diagram: - **O** is the origin point at one end of the beam. The coordinates are aligned such that the Y-axis runs along the length of the beam. - **A** and **B** are labeled points on the beam: - **A** is at the top right corner of the front face. - **B** is at the bottom of the front face, where a force **F** is applied. - **F** represents a force acting perpendicular to the surface at point **B**. The arrow indicates the direction of the force application. - The length of the beam along the Y-axis is labeled as **8 ft**. - The vertical distance from the point **B** to the top of the beam is **1.5 ft**. - The horizontal distance from point **O** to the edge of the beam along the X-axis is **0.25 ft**. This diagram is often used in structural engineering to analyze the effects of forces applied at specific points on a beam, helping in stress and load distribution calculations.
**Problem Statement:**

Calculate the moment of force about:
A) Point O
B) Point A

Given that the applied force is \( \mathbf{F} = 450\mathbf{i} - 150\mathbf{j} - 350\mathbf{k} \).

**Diagram Description:**

- The diagram shows a three-dimensional L-shaped bar with dimensions:
  - Horizontal length along the y-axis: 8 ft
  - Vertical length along the z-axis: 1.5 ft
  - Width along the x-axis: 0.25 ft

- Points:
  - Point O is at the end of the horizontal bar on the y-axis.
  - Point B is at the junction of the vertical and horizontal bars.
  - Point A is at the top end of the vertical section along the z-axis.

- Applied Force, \( \mathbf{F} \), acts at point B and is directed in a direction not aligned with any primary axis, having components along \( \mathbf{i} \), \( \mathbf{j} \), and \( \mathbf{k} \).

**Explanation of Relevant Concepts:**

- The moment of a force about a point is calculated using the cross product \( \mathbf{M} = \mathbf{r} \times \mathbf{F} \).

- \( \mathbf{r} \) is the position vector from the point to where the force is applied.

**Steps for Calculation:**

1. **Moment about Point O:**
   - Determine the position vector \( \mathbf{r}_{O} \) from O to B.
   - Calculate \( \mathbf{M}_{O} = \mathbf{r}_{O} \times \mathbf{F} \).

2. **Moment about Point A:**
   - Determine the position vector \( \mathbf{r}_{A} \) from A to B.
   - Calculate \( \mathbf{M}_{A} = \mathbf{r}_{A} \times \mathbf{F} \).
   
These moments would provide scalar or vector expressions representing the rotational effect of the force about the specified points.
Transcribed Image Text:**Problem Statement:** Calculate the moment of force about: A) Point O B) Point A Given that the applied force is \( \mathbf{F} = 450\mathbf{i} - 150\mathbf{j} - 350\mathbf{k} \). **Diagram Description:** - The diagram shows a three-dimensional L-shaped bar with dimensions: - Horizontal length along the y-axis: 8 ft - Vertical length along the z-axis: 1.5 ft - Width along the x-axis: 0.25 ft - Points: - Point O is at the end of the horizontal bar on the y-axis. - Point B is at the junction of the vertical and horizontal bars. - Point A is at the top end of the vertical section along the z-axis. - Applied Force, \( \mathbf{F} \), acts at point B and is directed in a direction not aligned with any primary axis, having components along \( \mathbf{i} \), \( \mathbf{j} \), and \( \mathbf{k} \). **Explanation of Relevant Concepts:** - The moment of a force about a point is calculated using the cross product \( \mathbf{M} = \mathbf{r} \times \mathbf{F} \). - \( \mathbf{r} \) is the position vector from the point to where the force is applied. **Steps for Calculation:** 1. **Moment about Point O:** - Determine the position vector \( \mathbf{r}_{O} \) from O to B. - Calculate \( \mathbf{M}_{O} = \mathbf{r}_{O} \times \mathbf{F} \). 2. **Moment about Point A:** - Determine the position vector \( \mathbf{r}_{A} \) from A to B. - Calculate \( \mathbf{M}_{A} = \mathbf{r}_{A} \times \mathbf{F} \). These moments would provide scalar or vector expressions representing the rotational effect of the force about the specified points.
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