As shown in the figure below, two masses m1 = 4.20kg and m2 which has a mass 50.0% that of m1, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m1 and m2 start from rest, after they have each traveled a distance h = 2.20m, use energy content to determine the following. (a) speed v of the masses m/s (b) magnitude of the tension T in the cord N

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As shown in the figure below, two masses m1 = 4.20kg and m2 which has a mass 50.0% that of m1, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m1 and m2 start from rest, after they have each traveled a distance h = 2.20m, use energy content to determine the following.

(a) speed v of the masses m/s

(b) magnitude of the tension T in the cord N

### Simple Pulley System

#### Description:
This diagram illustrates a simple pulley system used in classical mechanics to study the forces and motion involved. The system consists of two masses, \( m_1 \) and \( m_2 \), connected by a string that passes over a frictionless pulley.

#### Components of the diagram:
1. **Pulley:**
   - Positioned at the top center of the diagram.
   - Assumed to be frictionless, meaning it does not resist the motion of the string passing over it.

2. **String:**
   - Connects the two masses and passes over the pulley.
   - Assumed to be light and inextensible, meaning its mass is negligible, and it does not stretch.

3. **Masses:**
   - \( m_1 \): On the right side, hanging downward.
   - \( m_2 \): On the left side, also hanging downward.
   - These masses are connected through the string on either side of the pulley.

4. **Distance \( h \):**
   - Represents the vertical distance between mass \( m_1 \) and the reference ground level.
   - Indicated by a dashed line vertically aligned with \( m_1 \).

#### Explanation:
- When released, the masses \( m_1 \) and \( m_2 \) will accelerate due to the force of gravity.
- If \( m_1 \) is heavier (has a greater gravitational force), \( m_1 \) will move downward, pulling \( m_2 \) upward.
- Conversely, if \( m_2 \) is heavier, it will move downward, pulling \( m_1 \) upward.
- The acceleration of the masses depends on the difference in their weights and can be analyzed using Newton's Second Law.

#### Equations:
For such a system, the accelerations and tensions can be described using the following equations of motion:

\[ m_1 g - T = m_1 a \]
\[ T - m_2 g = m_2 a \]

where:
- \( g \) is the acceleration due to gravity,
- \( T \) is the tension in the string,
- \( a \) is the acceleration of the masses.

By solving these equations simultaneously, you can determine the acceleration \( a \) and the tension \( T \) in the string.
Transcribed Image Text:### Simple Pulley System #### Description: This diagram illustrates a simple pulley system used in classical mechanics to study the forces and motion involved. The system consists of two masses, \( m_1 \) and \( m_2 \), connected by a string that passes over a frictionless pulley. #### Components of the diagram: 1. **Pulley:** - Positioned at the top center of the diagram. - Assumed to be frictionless, meaning it does not resist the motion of the string passing over it. 2. **String:** - Connects the two masses and passes over the pulley. - Assumed to be light and inextensible, meaning its mass is negligible, and it does not stretch. 3. **Masses:** - \( m_1 \): On the right side, hanging downward. - \( m_2 \): On the left side, also hanging downward. - These masses are connected through the string on either side of the pulley. 4. **Distance \( h \):** - Represents the vertical distance between mass \( m_1 \) and the reference ground level. - Indicated by a dashed line vertically aligned with \( m_1 \). #### Explanation: - When released, the masses \( m_1 \) and \( m_2 \) will accelerate due to the force of gravity. - If \( m_1 \) is heavier (has a greater gravitational force), \( m_1 \) will move downward, pulling \( m_2 \) upward. - Conversely, if \( m_2 \) is heavier, it will move downward, pulling \( m_1 \) upward. - The acceleration of the masses depends on the difference in their weights and can be analyzed using Newton's Second Law. #### Equations: For such a system, the accelerations and tensions can be described using the following equations of motion: \[ m_1 g - T = m_1 a \] \[ T - m_2 g = m_2 a \] where: - \( g \) is the acceleration due to gravity, - \( T \) is the tension in the string, - \( a \) is the acceleration of the masses. By solving these equations simultaneously, you can determine the acceleration \( a \) and the tension \( T \) in the string.
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