An Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. The masses have the values \( m_1 = 23.0 \, \text{kg} \) and \( m_2 = 12.0 \, \text{kg} \). Assume that the rope and pulley are massless and that there is no friction in the pulley. **Question:** What is the magnitude of the masses' acceleration \( a \)? \[ a = \, \boxed{\phantom{0}} \, \text{m/s}^2 \] **Question:** What is the magnitude of the tension \( T \) in the rope? \[ T = \, \boxed{\phantom{0}} \, \text{N} \] **Diagram Explanation:** The diagram shows two masses, \( m_1 \) and \( m_2 \), suspended on opposite ends of a rope which runs over a pulley. \( m_1 \) is depicted as a larger mass compared to \( m_2 \), consistent with the given values, indicating \( m_1 \) will accelerate downward and \( m_2 \) will accelerate upward due to the difference in weights. The pulley is shown as a simple wheel over which the rope is looped, representing an idealized scenario with no friction or mass considerations for the pulley and rope.
An Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. The masses have the values \( m_1 = 23.0 \, \text{kg} \) and \( m_2 = 12.0 \, \text{kg} \). Assume that the rope and pulley are massless and that there is no friction in the pulley. **Question:** What is the magnitude of the masses' acceleration \( a \)? \[ a = \, \boxed{\phantom{0}} \, \text{m/s}^2 \] **Question:** What is the magnitude of the tension \( T \) in the rope? \[ T = \, \boxed{\phantom{0}} \, \text{N} \] **Diagram Explanation:** The diagram shows two masses, \( m_1 \) and \( m_2 \), suspended on opposite ends of a rope which runs over a pulley. \( m_1 \) is depicted as a larger mass compared to \( m_2 \), consistent with the given values, indicating \( m_1 \) will accelerate downward and \( m_2 \) will accelerate upward due to the difference in weights. The pulley is shown as a simple wheel over which the rope is looped, representing an idealized scenario with no friction or mass considerations for the pulley and rope.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![An Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. The masses have the values \( m_1 = 23.0 \, \text{kg} \) and \( m_2 = 12.0 \, \text{kg} \). Assume that the rope and pulley are massless and that there is no friction in the pulley.
**Question:**
What is the magnitude of the masses' acceleration \( a \)?
\[ a = \, \boxed{\phantom{0}} \, \text{m/s}^2 \]
**Question:**
What is the magnitude of the tension \( T \) in the rope?
\[ T = \, \boxed{\phantom{0}} \, \text{N} \]
**Diagram Explanation:**
The diagram shows two masses, \( m_1 \) and \( m_2 \), suspended on opposite ends of a rope which runs over a pulley. \( m_1 \) is depicted as a larger mass compared to \( m_2 \), consistent with the given values, indicating \( m_1 \) will accelerate downward and \( m_2 \) will accelerate upward due to the difference in weights. The pulley is shown as a simple wheel over which the rope is looped, representing an idealized scenario with no friction or mass considerations for the pulley and rope.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b685a38-634a-4ae1-b9d6-59ae15f6a370%2Fc98eef54-2b6a-42b9-854a-b8f5deeb7564%2Fuisthxp.jpeg&w=3840&q=75)
Transcribed Image Text:An Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. The masses have the values \( m_1 = 23.0 \, \text{kg} \) and \( m_2 = 12.0 \, \text{kg} \). Assume that the rope and pulley are massless and that there is no friction in the pulley.
**Question:**
What is the magnitude of the masses' acceleration \( a \)?
\[ a = \, \boxed{\phantom{0}} \, \text{m/s}^2 \]
**Question:**
What is the magnitude of the tension \( T \) in the rope?
\[ T = \, \boxed{\phantom{0}} \, \text{N} \]
**Diagram Explanation:**
The diagram shows two masses, \( m_1 \) and \( m_2 \), suspended on opposite ends of a rope which runs over a pulley. \( m_1 \) is depicted as a larger mass compared to \( m_2 \), consistent with the given values, indicating \( m_1 \) will accelerate downward and \( m_2 \) will accelerate upward due to the difference in weights. The pulley is shown as a simple wheel over which the rope is looped, representing an idealized scenario with no friction or mass considerations for the pulley and rope.
Expert Solution
Step 1
Given:
The mass of the first block is .
The mass of the second block is .
Introduction:
The tension in a massless string is uniform throughout the length of the string. The tension in the string is due to the pulling nature of the force.
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Solved in 3 steps with 1 images
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