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Two blocks are positioned on surfaces, each inclined at the same angle of 52.8 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 4.60 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.530. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the LEFT

Two blocks are positioned on surfaces, each inclined at the same angle of 52.8 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 4.60 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.530. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the LEFT

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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Two blocks are positioned on surfaces, each inclined at the same angle of 52.8 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 4.60 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.530. Assume static friction has been overcome and that everything can slide. 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.
10.02 kg
  b.
2.94 kg
  c.
3.10 kg
  d.
18.07 kg
**Inclined Pulley System Diagram** In this diagram, we observe an inclined pulley system featuring two wedges and a single pulley placed at the peak of the inclines. **Components:** 1. **Inclined Planes:** There are two inclined planes, each inclined at an angle θ with respect to the horizontal. 2. **Pulley:** At the junction where the two inclined planes meet, there is a pulley mounted. 3. **Blocks:** Two blocks are shown on opposite sides of the pulley. The block on the left side of the diagram appears to be plain, while the block on the right side is shaded. **Explanation:** - The **inclined planes** create sloped surfaces that affect the motion of the blocks due to gravitational force. - The **pulley** allows a rope (or string) to pass over it, changing the direction of the force applied and potentially allowing the blocks to be connected. - On one side of the pulley, a **block** is placed on the inclined plane sloping downward to the left. On the opposite side of the pulley, another **block** is on an incline sloping downward to the right. - The inclines are symmetrical, both having the same angle denoted by θ. This symmetry indicates that the forces on both blocks might be considered under similar conditions of incline. This system can be used to study and demonstrate principles of mechanics such as tension, normal force, frictional force (if considered), gravitational force components, and how these forces interplay to influence the motion of the blocks. **Applications:** - This type of setup is often used in physics education to teach Newton's laws of motion and equilibrium. - It can help in understanding the vector components of forces in an inclined system and how pulleys are utilized to change the direction of forces in mechanical systems.
Transcribed Image Text:**Inclined Pulley System Diagram** In this diagram, we observe an inclined pulley system featuring two wedges and a single pulley placed at the peak of the inclines. **Components:** 1. **Inclined Planes:** There are two inclined planes, each inclined at an angle θ with respect to the horizontal. 2. **Pulley:** At the junction where the two inclined planes meet, there is a pulley mounted. 3. **Blocks:** Two blocks are shown on opposite sides of the pulley. The block on the left side of the diagram appears to be plain, while the block on the right side is shaded. **Explanation:** - The **inclined planes** create sloped surfaces that affect the motion of the blocks due to gravitational force. - The **pulley** allows a rope (or string) to pass over it, changing the direction of the force applied and potentially allowing the blocks to be connected. - On one side of the pulley, a **block** is placed on the inclined plane sloping downward to the left. On the opposite side of the pulley, another **block** is on an incline sloping downward to the right. - The inclines are symmetrical, both having the same angle denoted by θ. This symmetry indicates that the forces on both blocks might be considered under similar conditions of incline. This system can be used to study and demonstrate principles of mechanics such as tension, normal force, frictional force (if considered), gravitational force components, and how these forces interplay to influence the motion of the blocks. **Applications:** - This type of setup is often used in physics education to teach Newton's laws of motion and equilibrium. - It can help in understanding the vector components of forces in an inclined system and how pulleys are utilized to change the direction of forces in mechanical systems.
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