Two blocks of masses m1 and m2 are connected by a cord that passes over a pulley as shown in the figure below. They start at the same height, and the hanging block is lowered through a distance h, causing the block on the incline to rise. Calculate the change in gravitational potential energy for each of the blocks. (Use any variable or symbol stated above along with the following as necessary: g, θ. Include the sign of the value in your answer.)

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Two blocks of masses m1 and m2 are connected by a cord that passes over a pulley as shown in the figure below. They start at the same height, and the hanging block is lowered through a distance h, causing the block on the incline to rise. Calculate the change in gravitational potential energy for each of the blocks. (Use any variable or symbol stated above along with the following as necessary: g, θ. Include the sign of the value in your answer.)

The image depicts a classic physics problem involving a pulley system with two masses. Here's a detailed description:

1. **Pulley and Mass Setup**:
   - A pulley is mounted at the edge of an inclined plane.
   - A string passes over the pulley, connecting two masses, \( m_1 \) and \( m_2 \).

2. **Mass \( m_1 \)**:
   - Positioned vertically, hanging freely off the pulley.
   - Represented by a purple square.

3. **Mass \( m_2 \)**:
   - Positioned on the inclined plane.
   - Represented by a green square.
   - The inclined plane forms an angle \( \theta \) with the horizontal.

4. **Inclined Plane**:
   - The plane is sloped, and mass \( m_2 \) rests on it.
   - The angle \( \theta \) is labeled, indicating the slope of the plane.

**System Dynamics**:
- Both masses are connected by a string over the pulley, indicating a system where the movement of one mass will affect the other.
- The direction of potential movement is shown: \( m_1 \) is likely to move downward due to gravity, while \( m_2 \) may slide up or down the incline, depending on different factors such as masses and friction.

**Educational Context**:
- This setup is commonly used to teach concepts of Newtonian mechanics, including gravitational force, tension in a string, normal force, and friction on an inclined plane. The angle \( \theta \) introduces trigonometric analysis for decomposing forces.
Transcribed Image Text:The image depicts a classic physics problem involving a pulley system with two masses. Here's a detailed description: 1. **Pulley and Mass Setup**: - A pulley is mounted at the edge of an inclined plane. - A string passes over the pulley, connecting two masses, \( m_1 \) and \( m_2 \). 2. **Mass \( m_1 \)**: - Positioned vertically, hanging freely off the pulley. - Represented by a purple square. 3. **Mass \( m_2 \)**: - Positioned on the inclined plane. - Represented by a green square. - The inclined plane forms an angle \( \theta \) with the horizontal. 4. **Inclined Plane**: - The plane is sloped, and mass \( m_2 \) rests on it. - The angle \( \theta \) is labeled, indicating the slope of the plane. **System Dynamics**: - Both masses are connected by a string over the pulley, indicating a system where the movement of one mass will affect the other. - The direction of potential movement is shown: \( m_1 \) is likely to move downward due to gravity, while \( m_2 \) may slide up or down the incline, depending on different factors such as masses and friction. **Educational Context**: - This setup is commonly used to teach concepts of Newtonian mechanics, including gravitational force, tension in a string, normal force, and friction on an inclined plane. The angle \( \theta \) introduces trigonometric analysis for decomposing forces.
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