Consider a block on a level track attached to a mass hanging from a pulley. If the track is not frictionless, some kinetic energy will be lost to friction as the blocks move. Derive the expression for the work done by friction on the block moving along the track. Also derive the expression for the coefficient of friction from the work

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Consider a block on a level track attached to a mass hanging from a pulley. If the track is not frictionless, some kinetic energy will be lost to friction as the blocks move. Derive the expression for the work done by friction on the block moving along the track. Also derive the expression for the coefficient of friction from the work.

 
This image depicts a physics system consisting of two masses connected by a pulley mechanism on a flat surface.

- **Mass \( M_1 \):** This block is placed on a horizontal surface, which seems to be a frictionless table. The mass is labeled as \( M_1 \).

- **Pulley System:** To the right of \( M_1 \), there's a fixed pulley. The pulley changes the direction of the tension in the rope, allowing the force exerted by the hanging mass to influence \( M_1 \).

- **Mass \( M_2 \):** This block is hanging vertically, suspended by a rope running over the pulley. It is labeled as \( M_2 \).

- **Support System:** The table appears to be supported by a triangular support structure beneath it, indicating stability despite the movement of masses.

This setup is commonly used in physics to demonstrate concepts such as Newton's laws of motion, tension in strings, and gravitational force. When \( M_2 \) is acted upon by gravity, it creates tension in the rope, which pulls \( M_1 \) horizontally. This scenario can be analyzed to calculate the acceleration of the system and the tension in the rope.
Transcribed Image Text:This image depicts a physics system consisting of two masses connected by a pulley mechanism on a flat surface. - **Mass \( M_1 \):** This block is placed on a horizontal surface, which seems to be a frictionless table. The mass is labeled as \( M_1 \). - **Pulley System:** To the right of \( M_1 \), there's a fixed pulley. The pulley changes the direction of the tension in the rope, allowing the force exerted by the hanging mass to influence \( M_1 \). - **Mass \( M_2 \):** This block is hanging vertically, suspended by a rope running over the pulley. It is labeled as \( M_2 \). - **Support System:** The table appears to be supported by a triangular support structure beneath it, indicating stability despite the movement of masses. This setup is commonly used in physics to demonstrate concepts such as Newton's laws of motion, tension in strings, and gravitational force. When \( M_2 \) is acted upon by gravity, it creates tension in the rope, which pulls \( M_1 \) horizontally. This scenario can be analyzed to calculate the acceleration of the system and the tension in the rope.
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