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Two blocks are positioned on surfaces, each inclined at the same angle of 46.3 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 5.99 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.330. 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 RIGHT at a constant velocity?

Two blocks are positioned on surfaces, each inclined at the same angle of 46.3 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 5.99 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.330. 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 RIGHT at a constant velocity?

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  1. Two blocks are positioned on surfaces, each inclined at the same angle of 46.3 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 5.99 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.330. 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 RIGHT at a constant velocity?

      a.

    4.56 kg
      b.

    11.51 kg
      c.

    3.12 kg
      d.

    5.99 kg

2. 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 3.35 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.270. 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 a constant velocity?

  a.

3.35 kg
  b.

4.22 kg
  c.

2.21 kg
  d.

5.08 kg
The diagram illustrates a mechanical system involving two blocks connected by a string over a pulley, set on a symmetrical inclined plane. Key components and labels include: 1. **Two Blocks**: The diagram shows two blocks, one positioned on the left and the other on the right side of a triangular-shaped inclined plane. 2. **Inclined Plane**: The inclined plane is symmetrical, meaning both sides have equal angles of inclination (denoted by θ) with respect to the horizontal base level. 3. **Pulley System**: The blocks are connected via a string that runs over a small pulley located at the apex or the top of the inclined plane. 4. **Angle of Inclination (θ)**: Both the left and right sides of the inclined plane have the same angle θ, forming the two symmetrical slopes. ### Explanation: In this setup: - The left block sits on the left incline and the right block on the right incline. - Due to the symmetrical nature of the inclined plane, both blocks experience gravitational forces causing them to slide downwards along the respective inclines. - The string transmits the forces between the two blocks through the pulley, which balances the system depending upon the masses of the blocks and the angles of inclination (θ). This system is essential to understand the principles of mechanics, particularly in studying static equilibrium, tension in strings, and the role of gravitational force on inclined planes.
Transcribed Image Text:The diagram illustrates a mechanical system involving two blocks connected by a string over a pulley, set on a symmetrical inclined plane. Key components and labels include: 1. **Two Blocks**: The diagram shows two blocks, one positioned on the left and the other on the right side of a triangular-shaped inclined plane. 2. **Inclined Plane**: The inclined plane is symmetrical, meaning both sides have equal angles of inclination (denoted by θ) with respect to the horizontal base level. 3. **Pulley System**: The blocks are connected via a string that runs over a small pulley located at the apex or the top of the inclined plane. 4. **Angle of Inclination (θ)**: Both the left and right sides of the inclined plane have the same angle θ, forming the two symmetrical slopes. ### Explanation: In this setup: - The left block sits on the left incline and the right block on the right incline. - Due to the symmetrical nature of the inclined plane, both blocks experience gravitational forces causing them to slide downwards along the respective inclines. - The string transmits the forces between the two blocks through the pulley, which balances the system depending upon the masses of the blocks and the angles of inclination (θ). This system is essential to understand the principles of mechanics, particularly in studying static equilibrium, tension in strings, and the role of gravitational force on inclined planes.
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