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Determine the reactions at the roller B, the rocker C, and where the beam contacts the smooth plane at A. Neglect the thickness of the beam. Suppose that F₁ = 250 N and F2 = 400 N. 5 L. 4 m F₁ B -2 m- F₂ 60° -6 m-

Determine the reactions at the roller B, the rocker C, and where the beam contacts the smooth plane at A. Neglect the thickness of the beam. Suppose that F₁ = 250 N and F2 = 400 N. 5 L. 4 m F₁ B -2 m- F₂ 60° -6 m-

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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5. Based on the attached figure: - Determine the y-component of the reaction at roller B and rocker C. (FB)Y = ? , (FC)Y = ? - Determine the magnitude of the reaction at A. F(A) = ?
**Title: Analyzing Beam Reactions on a Smooth Plane** **Objective:** The goal is to determine the reactions at various points of support for a beam: the roller at point \( B \), the rocker at point \( C \), and the contact point \( A \) on a smooth inclined plane. We will assume the thickness of the beam is negligible. **Given Forces:** - Force \( F_1 = 250\, \text{N} \) - Force \( F_2 = 400\, \text{N} \) acting at an angle of \( 60^\circ \) **Beam Configuration:** - Point \( A \) is at the intersection of the beam and the inclined plane, which forms a \( 3:4:5 \) triangle with the surface. - The distance from \( A \) to \( B \) is \( 4\, \text{m} \). - The distance from \( B \) to \( C \) is \( 6\, \text{m} \). - The distance from \( B \) to the point where \( F_1 \) acts is \( 2\, \text{m} \). **Diagram Explanation:** The diagram depicts a beam resting on different support points: - **Inclined Plane**: The beam makes contact at point \( A \), where the inclination forms a \( 3:4:5 \) triangle. - **Roller Support**: Located at point \( B \), allows horizontal movement but not vertical. - **Rocker Support**: Positioned at point \( C \), also allowing for rotation or tilting, but not horizontal or vertical sliding. Two forces are applied: - **Force \( F_1\)** acts vertically downward at a point between \( A \) and \( B \). - **Force \( F_2\)** acts downward at a \( 60^\circ \) angle to the horizontal. **Objective Breakdown:** 1. Calculate the reactions at point \( B \). 2. Calculate the reactions at point \( C \). 3. Calculate the reaction at the contact point \( A \). **Conclusion:** This setup models real-world physical scenarios where structures rest on various supports. The reactions calculated at these points will help understand the stress and distribution of forces within the system.
Transcribed Image Text:**Title: Analyzing Beam Reactions on a Smooth Plane** **Objective:** The goal is to determine the reactions at various points of support for a beam: the roller at point \( B \), the rocker at point \( C \), and the contact point \( A \) on a smooth inclined plane. We will assume the thickness of the beam is negligible. **Given Forces:** - Force \( F_1 = 250\, \text{N} \) - Force \( F_2 = 400\, \text{N} \) acting at an angle of \( 60^\circ \) **Beam Configuration:** - Point \( A \) is at the intersection of the beam and the inclined plane, which forms a \( 3:4:5 \) triangle with the surface. - The distance from \( A \) to \( B \) is \( 4\, \text{m} \). - The distance from \( B \) to \( C \) is \( 6\, \text{m} \). - The distance from \( B \) to the point where \( F_1 \) acts is \( 2\, \text{m} \). **Diagram Explanation:** The diagram depicts a beam resting on different support points: - **Inclined Plane**: The beam makes contact at point \( A \), where the inclination forms a \( 3:4:5 \) triangle. - **Roller Support**: Located at point \( B \), allows horizontal movement but not vertical. - **Rocker Support**: Positioned at point \( C \), also allowing for rotation or tilting, but not horizontal or vertical sliding. Two forces are applied: - **Force \( F_1\)** acts vertically downward at a point between \( A \) and \( B \). - **Force \( F_2\)** acts downward at a \( 60^\circ \) angle to the horizontal. **Objective Breakdown:** 1. Calculate the reactions at point \( B \). 2. Calculate the reactions at point \( C \). 3. Calculate the reaction at the contact point \( A \). **Conclusion:** This setup models real-world physical scenarios where structures rest on various supports. The reactions calculated at these points will help understand the stress and distribution of forces within the system.
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