Two masses, m1 and m2 are connected by a frictionless pulley and a massless string (ideal pulley system). One mass, m1 sits on a 25o incline that is also frictionless, the other mass is suspended in air, as shown in figure 2. The mass on the incline (m1) has a mass of 5kg. Both masses are at rest. a) Draw a free-body diagram for both masses. b) What is the value of m2?

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Two masses, m1 and m2 are connected by a frictionless pulley and a massless string (ideal
pulley system). One mass, m1 sits on a 25o incline that is also frictionless, the other mass is
suspended in air, as shown in figure 2. The mass on the incline (m1) has a mass of 5kg. Both
masses are at rest.
a) Draw a free-body diagram for both masses.
b) What is the value of m2?

 

**Inclined Plane Dynamics**

**Explanation of the Diagram:**

The image presents a classic physics problem involving an inclined plane and a pulley system, labeled as Figure 2. Here's a detailed breakdown:

1. **Inclined Plane:**
   - The inclined plane is set at an angle of \( 25^\circ \) to the horizontal.
   - A block with a mass of \(5 \text{ kg}\) is positioned on the inclined plane. The block is connected to a string that goes over a pulley at the top of the inclined plane.

2. **Pulley System:**
   - The pulley is depicted as small and frictionless, placed at the top of the inclined plane.
   - The string running over the pulley connects two masses: the \( 5 \text{ kg} \) block on the inclined plane, and another mass labeled as \( m_2 \), which is hanging vertically on the left side of the pulley.

3. **Masses:**
   - The block on the incline has a specified mass of \(5 \text{ kg}\).
   - The mass \( m_2 \) is not specified in the diagram and is represented as an unknown variable.

**Applications in Physics:**
This diagram often forms the basis of problems to understand the mechanics of systems involving inclined planes and pulleys. Key concepts that can be explored using this setup include:

- **Forces Acting on Inclined Plane**: 
  - The gravitational force acting on the block can be resolved into components parallel and perpendicular to the inclined plane.
  - Tension in the string connecting the masses.

- **Newton's Second Law**:
  - Applying Newton’s second law to both masses, considering forces due to gravity, tension in the string, and friction (if any).

- **Equilibrium and Motion**:
  - Conditions for equilibrium where the system remains stationary.
  - Calculating acceleration of the masses if the system is released from rest.

This setup is fundamental in understanding the basics of classical mechanics and is widely used in educational scenarios to illustrate principles of dynamics and kinematics.
Transcribed Image Text:**Inclined Plane Dynamics** **Explanation of the Diagram:** The image presents a classic physics problem involving an inclined plane and a pulley system, labeled as Figure 2. Here's a detailed breakdown: 1. **Inclined Plane:** - The inclined plane is set at an angle of \( 25^\circ \) to the horizontal. - A block with a mass of \(5 \text{ kg}\) is positioned on the inclined plane. The block is connected to a string that goes over a pulley at the top of the inclined plane. 2. **Pulley System:** - The pulley is depicted as small and frictionless, placed at the top of the inclined plane. - The string running over the pulley connects two masses: the \( 5 \text{ kg} \) block on the inclined plane, and another mass labeled as \( m_2 \), which is hanging vertically on the left side of the pulley. 3. **Masses:** - The block on the incline has a specified mass of \(5 \text{ kg}\). - The mass \( m_2 \) is not specified in the diagram and is represented as an unknown variable. **Applications in Physics:** This diagram often forms the basis of problems to understand the mechanics of systems involving inclined planes and pulleys. Key concepts that can be explored using this setup include: - **Forces Acting on Inclined Plane**: - The gravitational force acting on the block can be resolved into components parallel and perpendicular to the inclined plane. - Tension in the string connecting the masses. - **Newton's Second Law**: - Applying Newton’s second law to both masses, considering forces due to gravity, tension in the string, and friction (if any). - **Equilibrium and Motion**: - Conditions for equilibrium where the system remains stationary. - Calculating acceleration of the masses if the system is released from rest. This setup is fundamental in understanding the basics of classical mechanics and is widely used in educational scenarios to illustrate principles of dynamics and kinematics.
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