Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Question
To test the strength of a 625 × 500-mm suitcase, forces are applied as shown. If \( P = 88 \, \text{N} \), (a) determine the resultant of the applied forces, (b) locate the two points where the line of action of the resultant intersects the edge of the suitcase. ### Diagram Explanation: The image shows a suitcase with dimensions of 625 mm in width and 500 mm in height. Four forces are applied at specific points on the suitcase: 1. **212 N Force:** Applied at point A (top-left edge) at a 45-degree angle upward. 2. **100 N Force:** Applied horizontally towards the right at point A (top-left edge). 3. **88 N Force (represented as P):** Applied vertically downward at point B, which is located 450 mm to the right of point A. 4. **180 N Force:** Applied vertically upward from point D, which is located 500 mm directly below point B (bottom-right edge). ### Dimensions Marked: 1. The point B is 450 mm horizontally to the right of point A. 2. The point D is 500 mm vertically below point B. ### Task: 1. **Determine the Resultant of the Applied Forces:** - Calculate the vector sum of the forces considering both magnitude and direction. 2. **Locate the Points where the Line of Action of the Resultant Intersects the Edge of the Suitcase:** - Identify the locations on the edge of the suitcase where the line of action of the resultant intersects. ### Points: - Point A: Top-left corner - Point B: 450 mm right from Point A - Point D: Bottom edge directly below Point B This explanation covers the necessary points, forces, and measurements involved in the problem as per the provided diagram.
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Transcribed Image Text:To test the strength of a 625 × 500-mm suitcase, forces are applied as shown. If \( P = 88 \, \text{N} \), (a) determine the resultant of the applied forces, (b) locate the two points where the line of action of the resultant intersects the edge of the suitcase. ### Diagram Explanation: The image shows a suitcase with dimensions of 625 mm in width and 500 mm in height. Four forces are applied at specific points on the suitcase: 1. **212 N Force:** Applied at point A (top-left edge) at a 45-degree angle upward. 2. **100 N Force:** Applied horizontally towards the right at point A (top-left edge). 3. **88 N Force (represented as P):** Applied vertically downward at point B, which is located 450 mm to the right of point A. 4. **180 N Force:** Applied vertically upward from point D, which is located 500 mm directly below point B (bottom-right edge). ### Dimensions Marked: 1. The point B is 450 mm horizontally to the right of point A. 2. The point D is 500 mm vertically below point B. ### Task: 1. **Determine the Resultant of the Applied Forces:** - Calculate the vector sum of the forces considering both magnitude and direction. 2. **Locate the Points where the Line of Action of the Resultant Intersects the Edge of the Suitcase:** - Identify the locations on the edge of the suitcase where the line of action of the resultant intersects. ### Points: - Point A: Top-left corner - Point B: 450 mm right from Point A - Point D: Bottom edge directly below Point B This explanation covers the necessary points, forces, and measurements involved in the problem as per the provided diagram.
**Analyzing Wind Loading on a Building Frame** **Problem Statement:** The roof of a building frame is subjected to the wind loading as depicted in the figure. The objectives are to determine: (a) The equivalent force-couple system at point D. (b) The resultant of the loading and its line of action. **Diagram Explanation:** The image shows a diagram of a building frame with specific wind load forces indicated. The structure appears to be symmetrical with a triangular roof peaked at point B. The forces applied are as follows: 1. At the left edge (beside point A): A downward force of 200 lbs. 2. Moving from left to right at equal distances of 10 ft: - First segment (left of peak): Downward forces of 400 lbs, 200 lbs, and upward force of 200 lbs. - Second segment (right of peak): Downward forces of 400 lbs, 200 lbs, and upward force of 200 lbs. 3. At the right edge (beside point E): A downward force of 200 lbs. The height measurements from the top of the frame to the bottom are also given - 20 ft total height and alternating 10 ft heights across different segments. By analyzing the applied forces symmetrically around the peak and knowing the dimensional properties, students can solve for the equivalent force-couple system at point D, as well as determine the overall resultant force and its line of action for a comprehensive understanding of the wind loading effects on the building frame.
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Transcribed Image Text:**Analyzing Wind Loading on a Building Frame** **Problem Statement:** The roof of a building frame is subjected to the wind loading as depicted in the figure. The objectives are to determine: (a) The equivalent force-couple system at point D. (b) The resultant of the loading and its line of action. **Diagram Explanation:** The image shows a diagram of a building frame with specific wind load forces indicated. The structure appears to be symmetrical with a triangular roof peaked at point B. The forces applied are as follows: 1. At the left edge (beside point A): A downward force of 200 lbs. 2. Moving from left to right at equal distances of 10 ft: - First segment (left of peak): Downward forces of 400 lbs, 200 lbs, and upward force of 200 lbs. - Second segment (right of peak): Downward forces of 400 lbs, 200 lbs, and upward force of 200 lbs. 3. At the right edge (beside point E): A downward force of 200 lbs. The height measurements from the top of the frame to the bottom are also given - 20 ft total height and alternating 10 ft heights across different segments. By analyzing the applied forces symmetrically around the peak and knowing the dimensional properties, students can solve for the equivalent force-couple system at point D, as well as determine the overall resultant force and its line of action for a comprehensive understanding of the wind loading effects on the building frame.
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