Two objects are positioned and moving as shown. m, = 5.9_kg, m2 = 8.7_kg, and the coefficient of kinetic friction between object 1 and the tabletop is µg = 0.18. Find the acceleration of object 2 (assuming up is the positive direction) as well as the tension in the string. motion m1 Th m2 Acceleration of Object 2: A. 3.826 m/s? D. 10.11 m/s? motion

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**Problem Statement**

Two objects are positioned and moving as shown in the diagram. Object \( m_1 = 5.9 \, \text{kg} \) is on a horizontal surface, and object \( m_2 = 8.7 \, \text{kg} \) is hanging vertically. The coefficient of kinetic friction \( \mu_k \) between object 1 and the tabletop is 0.18. The task is to find the acceleration of object 2 (assuming up is the positive direction) as well as the tension in the string.

**Diagram Description**

The diagram consists of two objects, \( m_1 \) and \( m_2 \). Object \( m_1 \) rests on a table, with motion indicated to the right. A string, passing over a pulley, connects \( m_1 \) to \( m_2 \). Object \( m_2 \) hangs vertically and has downward motion.

**Options for Acceleration of Object 2:**

A. \( 3.826 \, \text{m/s}^2 \)  
B. \( 4.736 \, \text{m/s}^2 \)  
C. \( 5.127 \, \text{m/s}^2 \)  
D. \( 10.11 \, \text{m/s}^2 \)  
E. \( 7.718 \, \text{m/s}^2 \)  
F. \( 8.554 \, \text{m/s}^2 \)  

**Options for Tension in the String:**

A. \( 64.11 \, \text{N} \)  
B. \( 77.25 \, \text{N} \)  
C. \( 52.07 \, \text{N} \)  
D. \( 74.38 \, \text{N} \)  
E. \( 40.66 \, \text{N} \)  
F. \( 57.04 \, \text{N} \)  

The problem involves analyzing the forces acting on both objects, considering the friction between the tabletop and object \( m_1 \), and using principles of physics to solve for the acceleration and tension.
Transcribed Image Text:**Problem Statement** Two objects are positioned and moving as shown in the diagram. Object \( m_1 = 5.9 \, \text{kg} \) is on a horizontal surface, and object \( m_2 = 8.7 \, \text{kg} \) is hanging vertically. The coefficient of kinetic friction \( \mu_k \) between object 1 and the tabletop is 0.18. The task is to find the acceleration of object 2 (assuming up is the positive direction) as well as the tension in the string. **Diagram Description** The diagram consists of two objects, \( m_1 \) and \( m_2 \). Object \( m_1 \) rests on a table, with motion indicated to the right. A string, passing over a pulley, connects \( m_1 \) to \( m_2 \). Object \( m_2 \) hangs vertically and has downward motion. **Options for Acceleration of Object 2:** A. \( 3.826 \, \text{m/s}^2 \) B. \( 4.736 \, \text{m/s}^2 \) C. \( 5.127 \, \text{m/s}^2 \) D. \( 10.11 \, \text{m/s}^2 \) E. \( 7.718 \, \text{m/s}^2 \) F. \( 8.554 \, \text{m/s}^2 \) **Options for Tension in the String:** A. \( 64.11 \, \text{N} \) B. \( 77.25 \, \text{N} \) C. \( 52.07 \, \text{N} \) D. \( 74.38 \, \text{N} \) E. \( 40.66 \, \text{N} \) F. \( 57.04 \, \text{N} \) The problem involves analyzing the forces acting on both objects, considering the friction between the tabletop and object \( m_1 \), and using principles of physics to solve for the acceleration and tension.
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