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In the figure the pulley has negligible mass, and both it and the inclined plane are frictionless. Block A has a mass of 1.1 kg, block B has a mass of 2.0 kg, and angle θ is 30 °. If the blocks are released from rest with the connecting cord taut, what is their total kinetic energy when block B has fallen 23 cm?

In the figure the pulley has negligible mass, and both it and the inclined plane are frictionless. Block A has a mass of 1.1 kg, block B has a mass of 2.0 kg, and angle θ is 30 °. If the blocks are released from rest with the connecting cord taut, what is their total kinetic energy when block B has fallen 23 cm?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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In the figure the pulley has negligible mass, and both it and the inclined plane are frictionless. Block A has a mass of 1.1 kg, block B has a mass of 2.0 kg, and angle θ is 30 °. If the blocks are released from rest with the connecting cord taut, what is their total kinetic energy when block B has fallen 23 cm?

### Understanding Inclined Planes and Pulleys #### Illustration Description The image illustrates a common physics problem involving an inclined plane and a pulley system. Here's a detailed description of the components and their arrangement: 1. **Objects A and B**: - **Object A** is a green block located on a slanted surface, representing an inclined plane. - **Object B** is a pink block hanging vertically off the edge of the inclined plane. 2. **Inclined Plane**: - The incline of the plane is marked by the angle \(\theta\) (theta), which denotes the angle between the inclined plane and the horizontal ground. 3. **Pulley System**: - The green block (Object A) is connected to the pink block (Object B) via a string and pulley arrangement. - A pulley is attached at the top of the inclined plane, changing the direction of the string connecting the two objects. - The string is assumed to be massless and inextensible, meaning it does not stretch and has negligible weight. #### Explanation of the Physics Concepts This setup can be used to study several fundamental concepts in physics, including: 1. **Forces on Inclined Planes**: - The component of gravitational force acting on block A along the inclined plane. - The normal force perpendicular to the surface of the inclined plane. 2. **Tension in the String**: - The tension in the string is the same throughout, given it is massless and the pulley is ideal (frictionless). 3. **Newton's Second Law**: - The acceleration of both blocks can be analyzed using Newton's second law, \( F = ma \). - Equations for the forces acting on blocks A and B can be set up to solve for unknown quantities such as acceleration, tension, etc. #### Example Problem 1. **Determine the acceleration**: - If the masses of blocks A and B are \( m_A \) and \( m_B \) respectively, one can determine their system’s acceleration. 2. **Equilibrium Condition**: - Analyze whether the system is in static or dynamic equilibrium, i.e., whether the blocks are moving or at rest. ### Conclusion This pulley-inclined plane setup is a classic example in physics used to understand the interplay of forces, motion, and equilibrium. Examining it helps in comprehending how different components such as
Transcribed Image Text:### Understanding Inclined Planes and Pulleys #### Illustration Description The image illustrates a common physics problem involving an inclined plane and a pulley system. Here's a detailed description of the components and their arrangement: 1. **Objects A and B**: - **Object A** is a green block located on a slanted surface, representing an inclined plane. - **Object B** is a pink block hanging vertically off the edge of the inclined plane. 2. **Inclined Plane**: - The incline of the plane is marked by the angle \(\theta\) (theta), which denotes the angle between the inclined plane and the horizontal ground. 3. **Pulley System**: - The green block (Object A) is connected to the pink block (Object B) via a string and pulley arrangement. - A pulley is attached at the top of the inclined plane, changing the direction of the string connecting the two objects. - The string is assumed to be massless and inextensible, meaning it does not stretch and has negligible weight. #### Explanation of the Physics Concepts This setup can be used to study several fundamental concepts in physics, including: 1. **Forces on Inclined Planes**: - The component of gravitational force acting on block A along the inclined plane. - The normal force perpendicular to the surface of the inclined plane. 2. **Tension in the String**: - The tension in the string is the same throughout, given it is massless and the pulley is ideal (frictionless). 3. **Newton's Second Law**: - The acceleration of both blocks can be analyzed using Newton's second law, \( F = ma \). - Equations for the forces acting on blocks A and B can be set up to solve for unknown quantities such as acceleration, tension, etc. #### Example Problem 1. **Determine the acceleration**: - If the masses of blocks A and B are \( m_A \) and \( m_B \) respectively, one can determine their system’s acceleration. 2. **Equilibrium Condition**: - Analyze whether the system is in static or dynamic equilibrium, i.e., whether the blocks are moving or at rest. ### Conclusion This pulley-inclined plane setup is a classic example in physics used to understand the interplay of forces, motion, and equilibrium. Examining it helps in comprehending how different components such as
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