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18-67. The system consists of a 30-kg disk, 12-kg slender rod BA, and a 5-kg smooth collar A. If the disk rolls without slipping, determine the velocity of the collar at the instant = 0°. The system is released from rest when 0 = 45°. A 2m B 0.5 m C 30°

18-67. The system consists of a 30-kg disk, 12-kg slender rod BA, and a 5-kg smooth collar A. If the disk rolls without slipping, determine the velocity of the collar at the instant = 0°. The system is released from rest when 0 = 45°. A 2m B 0.5 m C 30°

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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### Problem Statement **System Components:** - 30-kg disk - 12-kg slender rod \(AB\) - 5-kg smooth collar \(A\) **Objective:** Determine the velocity of the collar \(A\) at the instant when \(\theta = 0^\circ\), given that the disk rolls without slipping and the system is released from rest when \(\theta = 45^\circ\). **Initial Conditions & Constraints:** - The system is released from rest with \(\theta = 45^\circ\). - The disk rolls without slipping. - The initial angle of the inclined plane is \(30^\circ\). ### Diagram Analysis The diagram depicts a mechanical system consisting of three main components: 1. **Disk (B):** - Mass: 30 kg - Radius: 0.5 m 2. **Slender Rod (BA):** - Mass: 12 kg - Length: 2 m - Attached at point \(B\), and the other end is connected to a smooth collar \(A\). 3. **Smooth Collar (A):** - Mass: 5 kg - Moves along an inclined plane making an angle of \(30^\circ\) with the horizontal. **Notable Points on the Diagram:** - \(\theta\) represents the angle between the vertical axis and the rod BA. This angle changes dynamically as the system evolves. - Initially, \(\theta = 45^\circ\). ### Task Calculate the velocity of collar \(A\) precisely when \(\theta = 0^\circ\). This involves utilizing principles of dynamics, energy conservation, and kinematics, accounting for rolling without slipping of the disk.
Transcribed Image Text:### Problem Statement **System Components:** - 30-kg disk - 12-kg slender rod \(AB\) - 5-kg smooth collar \(A\) **Objective:** Determine the velocity of the collar \(A\) at the instant when \(\theta = 0^\circ\), given that the disk rolls without slipping and the system is released from rest when \(\theta = 45^\circ\). **Initial Conditions & Constraints:** - The system is released from rest with \(\theta = 45^\circ\). - The disk rolls without slipping. - The initial angle of the inclined plane is \(30^\circ\). ### Diagram Analysis The diagram depicts a mechanical system consisting of three main components: 1. **Disk (B):** - Mass: 30 kg - Radius: 0.5 m 2. **Slender Rod (BA):** - Mass: 12 kg - Length: 2 m - Attached at point \(B\), and the other end is connected to a smooth collar \(A\). 3. **Smooth Collar (A):** - Mass: 5 kg - Moves along an inclined plane making an angle of \(30^\circ\) with the horizontal. **Notable Points on the Diagram:** - \(\theta\) represents the angle between the vertical axis and the rod BA. This angle changes dynamically as the system evolves. - Initially, \(\theta = 45^\circ\). ### Task Calculate the velocity of collar \(A\) precisely when \(\theta = 0^\circ\). This involves utilizing principles of dynamics, energy conservation, and kinematics, accounting for rolling without slipping of the disk.
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