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The figure below shows two blocks connected by a string of negligible mass passing over a frictionless pulley. m1 = 6.4kg and ? = 12.0?. Assume that the incline is smooth.   (a) For what value of m2 the will the system be in equilibrium? m2 = kg   (b) If the block has to slide down the incline with an acceleration of 1.2m/s2, what should be the value of m2? m2 = kg

The figure below shows two blocks connected by a string of negligible mass passing over a frictionless pulley. m1 = 6.4kg and ? = 12.0?. Assume that the incline is smooth.   (a) For what value of m2 the will the system be in equilibrium? m2 = kg   (b) If the block has to slide down the incline with an acceleration of 1.2m/s2, what should be the value of m2? m2 = kg

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
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The figure below shows two blocks connected by a string of negligible mass passing over a frictionless pulley. m1 = 6.4kg and ? = 12.0?. Assume that the incline is smooth.

 

(a) For what value of m2 the will the system be in equilibrium? m2 = kg

 

(b) If the block has to slide down the incline with an acceleration of 1.2m/s2, what should be the value of m2? m2 = kg

The image illustrates a physics problem involving a system of two masses connected by a string over a pulley. Here's a detailed description for an educational website: --- ### Understanding Inclined Plane and Pulley Systems The diagram depicts a classic physics scenario used to understand the principles of mechanics, particularly Newton's laws of motion. **Components:** 1. **Inclined Plane:** This is depicted as a triangle with angle θ at the base. 2. **Masses:** - \(m_2\) is placed on the inclined plane. - \(m_1\) is hanging vertically off the pulley. 3. **Pulley:** A frictionless pulley at the top of the inclined plane over which a string is looped. 4. **String:** Assumed to be inextensible and massless, connecting \(m_1\) and \(m_2\). **Diagram Explanation:** - **Angle θ (Theta):** The angle of inclination of the plane relative to the horizontal. - **Block \(m_2\):** This block is positioned on the inclined plane and is connected via a string to mass \(m_1\). - **Block \(m_1\):** This block hangs vertically, exerting a downward force due to gravity. **Newton's Second Law in Action:** - Forces acting on \(m_2\): gravity component down the plane (\(m_2g \sin \theta\)), normal force perpendicular to the plane, and tension in the string. - Forces acting on \(m_1\): gravitational force \(m_1g\) downward and tension in the string upward. **Equations of Motion:** - For \(m_2\): \(m_2 a = m_2 g \sin \theta - T\) - For \(m_1\): \(m_1 a = T - m_1 g\) Where: - \(T\) is the tension in the string. - \(a\) is the acceleration of the system. **Purpose of Study:** - Analyzing such systems helps in understanding the concepts of equilibrium, acceleration, force distribution, and the interrelationship between mass, force, and acceleration in connected systems. This setup is integral for problem-solving in introductory physics courses and for understanding real-world applications, such as the mechanics involved in cable cars or cranes. --- This explanation will aid students in visualizing and conceptualizing the
Transcribed Image Text:The image illustrates a physics problem involving a system of two masses connected by a string over a pulley. Here's a detailed description for an educational website: --- ### Understanding Inclined Plane and Pulley Systems The diagram depicts a classic physics scenario used to understand the principles of mechanics, particularly Newton's laws of motion. **Components:** 1. **Inclined Plane:** This is depicted as a triangle with angle θ at the base. 2. **Masses:** - \(m_2\) is placed on the inclined plane. - \(m_1\) is hanging vertically off the pulley. 3. **Pulley:** A frictionless pulley at the top of the inclined plane over which a string is looped. 4. **String:** Assumed to be inextensible and massless, connecting \(m_1\) and \(m_2\). **Diagram Explanation:** - **Angle θ (Theta):** The angle of inclination of the plane relative to the horizontal. - **Block \(m_2\):** This block is positioned on the inclined plane and is connected via a string to mass \(m_1\). - **Block \(m_1\):** This block hangs vertically, exerting a downward force due to gravity. **Newton's Second Law in Action:** - Forces acting on \(m_2\): gravity component down the plane (\(m_2g \sin \theta\)), normal force perpendicular to the plane, and tension in the string. - Forces acting on \(m_1\): gravitational force \(m_1g\) downward and tension in the string upward. **Equations of Motion:** - For \(m_2\): \(m_2 a = m_2 g \sin \theta - T\) - For \(m_1\): \(m_1 a = T - m_1 g\) Where: - \(T\) is the tension in the string. - \(a\) is the acceleration of the system. **Purpose of Study:** - Analyzing such systems helps in understanding the concepts of equilibrium, acceleration, force distribution, and the interrelationship between mass, force, and acceleration in connected systems. This setup is integral for problem-solving in introductory physics courses and for understanding real-world applications, such as the mechanics involved in cable cars or cranes. --- This explanation will aid students in visualizing and conceptualizing the
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