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Member AB is supported at B by a cable and at A by a smooth fixed square rod which fits loosely through the square hole of the collar. If F = {20i - 40j - 75k} lb, determine the x, y, z components of reaction at A and the tension in the cable. 12 ft 8 ft 6 ft 4 ft

Member AB is supported at B by a cable and at A by a smooth fixed square rod which fits loosely through the square hole of the collar. If F = {20i - 40j - 75k} lb, determine the x, y, z components of reaction at A and the tension in the cable. 12 ft 8 ft 6 ft 4 ft

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### Problem Statement: Member \( AB \) is supported at \( B \) by a cable and at \( A \) by a smooth fixed square rod which fits loosely through the square hole of the collar. If \( \mathbf{F} = \{20\mathbf{i} - 40\mathbf{j} - 75\mathbf{k}\} \) lb, determine the \( x, y, z \) components of reaction at \( A \) and the tension in the cable. ### Diagram Explanation: The diagram shows a three-dimensional setup: - **Coordinate Axes:** - X-axis is horizontal, extending to the right. - Y-axis is horizontal, extending into the page. - Z-axis is vertical. - **Member \( AB \):** - The member \( AB \) is represented as a rigid bar positioned in a three-dimensional space. - It is supported at two points: \( A \) and \( B \). - **Support at \( A \):** - Point \( A \) is connected to a vertical rod, which allows the member to rotate but restricts lateral movement, indicating reactions in the x and y directions. - **Support at \( B \):** - Point \( B \) is attached to a cable, which is angled. - The cable extends from point \( B \) to point \( C \), which is on the z-axis 8 feet above the member. - **Dimensions:** - Length from \( A \) to \( B \) along the x-axis is 12 ft. - Length from \( B \) to the point on the z-axis below \( C \) is 4 ft. - Length from \( B \) vertically up to \( C \) is 6 ft. - The height from the base to \( C \) is given as 8 ft along the z-axis. - **Force \( \mathbf{F} \):** - An external force of \( \{20\mathbf{i} - 40\mathbf{j} - 75\mathbf{k}\} \) lb is applied at point \( B \), acting in three dimensions. ### Objective: To solve for the components of reaction at point \( A \) along the x, y, and z directions, and to determine the tension in the cable supporting member \( AB \) at point \( B \).
Transcribed Image Text:### Problem Statement: Member \( AB \) is supported at \( B \) by a cable and at \( A \) by a smooth fixed square rod which fits loosely through the square hole of the collar. If \( \mathbf{F} = \{20\mathbf{i} - 40\mathbf{j} - 75\mathbf{k}\} \) lb, determine the \( x, y, z \) components of reaction at \( A \) and the tension in the cable. ### Diagram Explanation: The diagram shows a three-dimensional setup: - **Coordinate Axes:** - X-axis is horizontal, extending to the right. - Y-axis is horizontal, extending into the page. - Z-axis is vertical. - **Member \( AB \):** - The member \( AB \) is represented as a rigid bar positioned in a three-dimensional space. - It is supported at two points: \( A \) and \( B \). - **Support at \( A \):** - Point \( A \) is connected to a vertical rod, which allows the member to rotate but restricts lateral movement, indicating reactions in the x and y directions. - **Support at \( B \):** - Point \( B \) is attached to a cable, which is angled. - The cable extends from point \( B \) to point \( C \), which is on the z-axis 8 feet above the member. - **Dimensions:** - Length from \( A \) to \( B \) along the x-axis is 12 ft. - Length from \( B \) to the point on the z-axis below \( C \) is 4 ft. - Length from \( B \) vertically up to \( C \) is 6 ft. - The height from the base to \( C \) is given as 8 ft along the z-axis. - **Force \( \mathbf{F} \):** - An external force of \( \{20\mathbf{i} - 40\mathbf{j} - 75\mathbf{k}\} \) lb is applied at point \( B \), acting in three dimensions. ### Objective: To solve for the components of reaction at point \( A \) along the x, y, and z directions, and to determine the tension in the cable supporting member \( AB \) at point \( B \).
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