5.2.50) In the diagram below, mị = 6.0kg, m2 = 3.0kg, and the coefficient of kinetic friction between mị and the surface on which it moves is 0.3. m2 is moving down. a) Draw free-body diagrams for each of the two masses. (You may draw free-body diagrams or either or both of the pulleys if you think it will be useful to do so.) Each free-body diagram hould include all force vectors acting on the object, as well as the object's acceleration vector. b) Find the acceleration of m2, and the tension in the string. mị m2

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Final Answer -> (5.2.50) 4.57 m/s2, 15.7 N  

**Problem (5.2.50):**

In the diagram below, \(m_1 = 6.0 \, \text{kg}\), \(m_2 = 3.0 \, \text{kg}\), and the coefficient of kinetic friction between \(m_1\) and the surface on which it moves is 0.3. \(m_2\) is moving down.

(a) Draw free-body diagrams for each of the two masses. (You may draw free-body diagrams for either or both of the pulleys if you think it will be useful to do so.) Each free-body diagram should include all force vectors acting on the object, as well as the object’s acceleration vector.

(b) Find the acceleration of \(m_2\), and the tension in the string.

**Diagram Explanation:**

- The diagram shows two masses, \(m_1\) and \(m_2\), connected by a string over a system of pulleys. 
- \(m_1\) is resting on a horizontal surface.
- \(m_2\) is hanging vertically off the edge of the surface.
- The string passes over two pulleys: one at the edge of the surface and one on the horizontal segment.

**Notes for Solving:**

- For free-body diagrams:
  - Include gravitational force, tension in the string, and frictional force for \(m_1\).
  - Include gravitational force and tension in the string for \(m_2\).
- Consider Newton's second law and the equations of motion.
- Use the coefficient of friction to determine the frictional force acting on \(m_1\).

**Important Concepts:**

- Kinetic friction: \( f_k = \mu_k \times N \), where \( N \) is the normal force.
- Net force and acceleration: \( F = ma \).
Transcribed Image Text:**Problem (5.2.50):** In the diagram below, \(m_1 = 6.0 \, \text{kg}\), \(m_2 = 3.0 \, \text{kg}\), and the coefficient of kinetic friction between \(m_1\) and the surface on which it moves is 0.3. \(m_2\) is moving down. (a) Draw free-body diagrams for each of the two masses. (You may draw free-body diagrams for either or both of the pulleys if you think it will be useful to do so.) Each free-body diagram should include all force vectors acting on the object, as well as the object’s acceleration vector. (b) Find the acceleration of \(m_2\), and the tension in the string. **Diagram Explanation:** - The diagram shows two masses, \(m_1\) and \(m_2\), connected by a string over a system of pulleys. - \(m_1\) is resting on a horizontal surface. - \(m_2\) is hanging vertically off the edge of the surface. - The string passes over two pulleys: one at the edge of the surface and one on the horizontal segment. **Notes for Solving:** - For free-body diagrams: - Include gravitational force, tension in the string, and frictional force for \(m_1\). - Include gravitational force and tension in the string for \(m_2\). - Consider Newton's second law and the equations of motion. - Use the coefficient of friction to determine the frictional force acting on \(m_1\). **Important Concepts:** - Kinetic friction: \( f_k = \mu_k \times N \), where \( N \) is the normal force. - Net force and acceleration: \( F = ma \).
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