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Two masses, m1 = .5 kg and m2 = .2 kg, are attached by a massless, unstretchable string which passes over a massless, frictionless pulley, as shown. A second string, attached to m2, is pulled horizontally to the right in order to accelerate the masses at 1.0 m/s2. Neglecting friction, determine the following: Now suppose there is friction between m2 and the table with coefficient of friction μ = .1. Draw two free body diagrams. c. If the tension T2 is the same as in part b, what is the new acceleration? d. What is T1?

Two masses, m1 = .5 kg and m2 = .2 kg, are attached by a massless, unstretchable string which passes over a massless, frictionless pulley, as shown. A second string, attached to m2, is pulled horizontally to the right in order to accelerate the masses at 1.0 m/s2. Neglecting friction, determine the following: Now suppose there is friction between m2 and the table with coefficient of friction μ = .1. Draw two free body diagrams. c. If the tension T2 is the same as in part b, what is the new acceleration? d. What is T1?

College Physics
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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Two masses, m1 = .5 kg and m2 = .2 kg, are attached by a
massless, unstretchable string which passes over a massless, frictionless pulley, as shown.
A second string, attached to m2, is pulled horizontally to the right in order to accelerate the masses at 1.0 m/s2. Neglecting friction, determine the following:

Now suppose there is friction between m2 and the table with coefficient of friction μ = .1. Draw two free body diagrams.
c. If the tension T2 is the same as in part b, what is the new acceleration?
d. What is T1?

### Physics of Pulley Systems #### Diagram Explanation: The diagram represents a common physics problem involving a pulley system. It demonstrates the interaction between two masses (m1 and m2) and the tensions (T1 and T2) in the ropes that connect them. - **Components:** 1. **Pulley:** A circular object around which a rope or cable runs. It changes the direction of the tension force in the rope without changing its magnitude. 2. **Mass \(m_1\):** This mass is hanging vertically, suspended by the rope. 3. **Mass \(m_2\):** This mass is resting on a horizontal surface, connected to the pulley system by the same rope that holds mass \(m_1\). 4. **Tension \(T_1\):** The tension in the portion of the rope connected to \(m_1\) and the pulley. 5. **Tension \(T_2\):** The tension in the portion of the rope connected to \(m_2\) and extending horizontally. - **Mechanics of the System:** - **Equilibrium Conditions:** - When the system is in equilibrium, the sum of forces acting on each mass must be zero. For \(m_1\), this includes its weight (\(m_1 \cdot g\)) and the tension \(T_1\). For \(m_2\), this includes the horizontal tension \(T_2\). - **Motion:** - If the system is not in equilibrium and is allowed to move, the masses will accelerate. The acceleration can be determined using Newton's Second Law (\(F = m \cdot a\)). Understanding the dynamics and forces in this pulley system is essential for students learning classical mechanics. Such problems help develop problem-solving skills and a deeper understanding of how forces interact in physical systems.
Transcribed Image Text:### Physics of Pulley Systems #### Diagram Explanation: The diagram represents a common physics problem involving a pulley system. It demonstrates the interaction between two masses (m1 and m2) and the tensions (T1 and T2) in the ropes that connect them. - **Components:** 1. **Pulley:** A circular object around which a rope or cable runs. It changes the direction of the tension force in the rope without changing its magnitude. 2. **Mass \(m_1\):** This mass is hanging vertically, suspended by the rope. 3. **Mass \(m_2\):** This mass is resting on a horizontal surface, connected to the pulley system by the same rope that holds mass \(m_1\). 4. **Tension \(T_1\):** The tension in the portion of the rope connected to \(m_1\) and the pulley. 5. **Tension \(T_2\):** The tension in the portion of the rope connected to \(m_2\) and extending horizontally. - **Mechanics of the System:** - **Equilibrium Conditions:** - When the system is in equilibrium, the sum of forces acting on each mass must be zero. For \(m_1\), this includes its weight (\(m_1 \cdot g\)) and the tension \(T_1\). For \(m_2\), this includes the horizontal tension \(T_2\). - **Motion:** - If the system is not in equilibrium and is allowed to move, the masses will accelerate. The acceleration can be determined using Newton's Second Law (\(F = m \cdot a\)). Understanding the dynamics and forces in this pulley system is essential for students learning classical mechanics. Such problems help develop problem-solving skills and a deeper understanding of how forces interact in physical systems.
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