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onsider a pulley system shown below. The coordinate x is the displacement of G. Assume there is no slip between the cord and the pulley, and disk and the ground.

onsider a pulley system shown below. The coordinate x is the displacement of G. Assume there is no slip between the cord and the pulley, and disk and the ground.

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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Consider a pulley system shown below. The coordinate x is the displacement of G. Assume there is no slip between the cord and the pulley, and disk and the ground.

 

What is the kinetic energy of the system? Select all that apply.

 

I don't know how to get these answers.

**Pulley System Analysis** Consider a pulley system as illustrated. The coordinate \(x\) indicates the displacement of point \(G\). Assume there is no slippage between the cord and both the pulley and disk with the ground. **Diagram Explanation:** - The system consists of a spring with spring constant \(k\), attached to a point on a lever or platform. - A disk of mass \(m_2\), radius \(R\), and center \(G\) rotates about point \(O\). - A mass \(m_1\) hangs from the pulley, moving vertically with coordinate \(y\). - The disk rotates with angle \(\theta\). The task is to determine the kinetic energy of the system. **Kinetic Energy Expressions:** 1. \( T = \frac{1}{2} m_1 \left( \frac{\dot{x}}{2} \right)^2 + \frac{1}{2} m_2 \dot{x}^2 + \frac{1}{2} \left( \frac{\dot{x}}{R} \right)^2 \) 2. \( T = \frac{1}{2} m_1 \dot{y}^2 + \frac{1}{2} m_2 \dot{x}^2 + \frac{1}{2} \dot{\theta}^2 \) **Note:** The selected answer includes both translational and rotational kinetic energy components, taking into account the various velocities and rotational rates in the system.
Transcribed Image Text:**Pulley System Analysis** Consider a pulley system as illustrated. The coordinate \(x\) indicates the displacement of point \(G\). Assume there is no slippage between the cord and both the pulley and disk with the ground. **Diagram Explanation:** - The system consists of a spring with spring constant \(k\), attached to a point on a lever or platform. - A disk of mass \(m_2\), radius \(R\), and center \(G\) rotates about point \(O\). - A mass \(m_1\) hangs from the pulley, moving vertically with coordinate \(y\). - The disk rotates with angle \(\theta\). The task is to determine the kinetic energy of the system. **Kinetic Energy Expressions:** 1. \( T = \frac{1}{2} m_1 \left( \frac{\dot{x}}{2} \right)^2 + \frac{1}{2} m_2 \dot{x}^2 + \frac{1}{2} \left( \frac{\dot{x}}{R} \right)^2 \) 2. \( T = \frac{1}{2} m_1 \dot{y}^2 + \frac{1}{2} m_2 \dot{x}^2 + \frac{1}{2} \dot{\theta}^2 \) **Note:** The selected answer includes both translational and rotational kinetic energy components, taking into account the various velocities and rotational rates in the system.
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