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Two blocks are positioned on surfaces, each inclined at the same angle of 57.5 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 5.50 kg, and this time there is NO friction. What is must be the mass of the white block if both blocks are to slide to the LEFT at an acceleration of 1.5 m/s^2?   a. 7.94 kg   b. 4.00 kg   c. 11.91 kg   d. 5.29 kg

Two blocks are positioned on surfaces, each inclined at the same angle of 57.5 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 5.50 kg, and this time there is NO friction. What is must be the mass of the white block if both blocks are to slide to the LEFT at an acceleration of 1.5 m/s^2?   a. 7.94 kg   b. 4.00 kg   c. 11.91 kg   d. 5.29 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
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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  1. Two blocks are positioned on surfaces, each inclined at the same angle of 57.5 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 5.50 kg, and this time there is NO friction. What is must be the mass of the white block if both blocks are to slide to the LEFT at an acceleration of 1.5 m/s^2?

      a.

    7.94 kg
      b.

    4.00 kg
      c.

    11.91 kg
      d.

    5.29 kg
### Physics of Inclined Planes and Connected Objects #### Diagram Explanation The diagram illustrates a classic physics problem involving inclined planes and objects connected by a pulley system. Here is a detailed explanation of the components and the setup: 1. **Inclined Planes**: The diagram features two inclined planes at symmetrical angles denoted as θ relative to the horizontal ground. Each inclined plane slopes upward and meets at a peak where the pulley is positioned. 2. **Pulley System**: At the peak of the two inclined planes, there is a pulley that allows the tension force to transfer from one object to another. The pulley is depicted as a small circle. 3. **Objects**: There are two objects involved in the diagram: - **Left Object**: This object is shown as a square box positioned on the left inclined plane. - **Right Object**: This one is depicted as a square box positioned on the right inclined plane but with a different design pattern to differentiate it from the left object. 4. **Connecting Rope**: A rope connects the two objects, passing over the pulley at the peak. This rope transmits the forces between the two objects due to their masses and the system's gravitational pull. #### Key Concepts - **Inclined Plane Angle (θ)**: The angle θ is crucial as it determines the component of gravitational force acting along the plane. For each object, the gravitational force can be split into two components – one perpendicular to the plane and one parallel to it. The parallel component (m*g*sin(θ), where m is the mass of the object and g is the gravitational acceleration) influences the motion of the object along the plane. - **Tension in the Rope**: The tension force in the rope is uniform and acts along the length of the rope. It helps balance the forces between the two objects. The tension force will depend on the masses of the objects and the angles of the inclined planes. - **Friction**: Although not explicitly marked, friction between the objects and the inclined planes can play a significant role in the system's dynamics, affecting the net acceleration and tension. #### Solving the System When solving this system, the following steps are usually taken: 1. **Force Analysis**: Break down the forces acting on each object, including gravitational forces, tension in the rope, and frictional forces (if applicable). 2. **Equations of Motion**: Using Newton's second law (F
Transcribed Image Text:### Physics of Inclined Planes and Connected Objects #### Diagram Explanation The diagram illustrates a classic physics problem involving inclined planes and objects connected by a pulley system. Here is a detailed explanation of the components and the setup: 1. **Inclined Planes**: The diagram features two inclined planes at symmetrical angles denoted as θ relative to the horizontal ground. Each inclined plane slopes upward and meets at a peak where the pulley is positioned. 2. **Pulley System**: At the peak of the two inclined planes, there is a pulley that allows the tension force to transfer from one object to another. The pulley is depicted as a small circle. 3. **Objects**: There are two objects involved in the diagram: - **Left Object**: This object is shown as a square box positioned on the left inclined plane. - **Right Object**: This one is depicted as a square box positioned on the right inclined plane but with a different design pattern to differentiate it from the left object. 4. **Connecting Rope**: A rope connects the two objects, passing over the pulley at the peak. This rope transmits the forces between the two objects due to their masses and the system's gravitational pull. #### Key Concepts - **Inclined Plane Angle (θ)**: The angle θ is crucial as it determines the component of gravitational force acting along the plane. For each object, the gravitational force can be split into two components – one perpendicular to the plane and one parallel to it. The parallel component (m*g*sin(θ), where m is the mass of the object and g is the gravitational acceleration) influences the motion of the object along the plane. - **Tension in the Rope**: The tension force in the rope is uniform and acts along the length of the rope. It helps balance the forces between the two objects. The tension force will depend on the masses of the objects and the angles of the inclined planes. - **Friction**: Although not explicitly marked, friction between the objects and the inclined planes can play a significant role in the system's dynamics, affecting the net acceleration and tension. #### Solving the System When solving this system, the following steps are usually taken: 1. **Force Analysis**: Break down the forces acting on each object, including gravitational forces, tension in the rope, and frictional forces (if applicable). 2. **Equations of Motion**: Using Newton's second law (F
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