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If B goes down with a speed v³ = 12 m/s, what is the speed of A? ·x A O VA = 2.4 m/s Ο UA = 2 m/s Ο UA = 1.2 m/s O VA = 3 m/s B

If B goes down with a speed v³ = 12 m/s, what is the speed of A? ·x A O VA = 2.4 m/s Ο UA = 2 m/s Ο UA = 1.2 m/s O VA = 3 m/s B

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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**Mechanics and Pulley Systems** ### Problem Statement **Question:** If \( B \) goes down with a speed \( v_B = 12 \text{ m/s} \), what is the speed of \( A \)? ### Description of the Setup A mechanical system involving a block \( A \) and a block \( B \) connected through a series of pulleys is shown in the illustration. Block \( A \) is linked to a set of five pulleys attached to the ceiling, whereas block \( B \) is suspended and can move vertically downward. The investigation aims to discern the speed of block \( A \) given that block \( B \) descends at a speed of \( 12 \text{ m/s} \). ### Diagram Explanation The image illustrates: - A block \( A \) connected to multiple pulleys (three on the left side and two on the right). - A block \( B \) hanging on the right side with a cable passing through the rightmost pulley. - These pulleys are mounted on a fixed frame at the top. - The rope moves through these pulleys, causing block \( A \) to move left-right while block \( B \) moves up-down. ### Options 1. \( v_A = 2.4 \text{ m/s} \) 2. \( v_A = 2 \text{ m/s} \) 3. \( v_A = 1.2 \text{ m/s} \) 4. \( v_A = 3 \text{ m/s} \) --- **Mechanical Concept Involved** The speeds in a pulley system are often related by the geometry and the number of pulleys involved. In this case, a certain ratio governs the relationship between the velocities of \( A \) and \( B \). Understanding the constraint equations derived from the pulley setup is fundamental to solve this problem. --- **Solution Approach (Hints)** 1. **Ratio of Distances**: Given the tracking of the cable's length on each segment, deduce how the movement of \( A \) translates to the movement in \( B \). 2. **Speed Relationship**: Use the physical relation derived from the distances to identify \( v_A \). Given \( B \) moves downward at \( 12 \text{ m/s} \), compute \( v_A \) by considering the mechanics involved in the setup. --- By understanding the
Transcribed Image Text:**Mechanics and Pulley Systems** ### Problem Statement **Question:** If \( B \) goes down with a speed \( v_B = 12 \text{ m/s} \), what is the speed of \( A \)? ### Description of the Setup A mechanical system involving a block \( A \) and a block \( B \) connected through a series of pulleys is shown in the illustration. Block \( A \) is linked to a set of five pulleys attached to the ceiling, whereas block \( B \) is suspended and can move vertically downward. The investigation aims to discern the speed of block \( A \) given that block \( B \) descends at a speed of \( 12 \text{ m/s} \). ### Diagram Explanation The image illustrates: - A block \( A \) connected to multiple pulleys (three on the left side and two on the right). - A block \( B \) hanging on the right side with a cable passing through the rightmost pulley. - These pulleys are mounted on a fixed frame at the top. - The rope moves through these pulleys, causing block \( A \) to move left-right while block \( B \) moves up-down. ### Options 1. \( v_A = 2.4 \text{ m/s} \) 2. \( v_A = 2 \text{ m/s} \) 3. \( v_A = 1.2 \text{ m/s} \) 4. \( v_A = 3 \text{ m/s} \) --- **Mechanical Concept Involved** The speeds in a pulley system are often related by the geometry and the number of pulleys involved. In this case, a certain ratio governs the relationship between the velocities of \( A \) and \( B \). Understanding the constraint equations derived from the pulley setup is fundamental to solve this problem. --- **Solution Approach (Hints)** 1. **Ratio of Distances**: Given the tracking of the cable's length on each segment, deduce how the movement of \( A \) translates to the movement in \( B \). 2. **Speed Relationship**: Use the physical relation derived from the distances to identify \( v_A \). Given \( B \) moves downward at \( 12 \text{ m/s} \), compute \( v_A \) by considering the mechanics involved in the setup. --- By understanding the
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