In the figure, block 1 has mass m, = 479 g, block 2 has mass m2 = 512 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.09 cm. When released from rest, block 2 falls 77.6 cm in 5.13 s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T2 (the tension force on the block 2) and (c) tension T, (the tension force on the block 1)? (d) What is the magnitude of the pulley's angular acceleration? (e) What is its rotational inertia? Caution: Try to avoid rounding off answers along the way to the solution. Use g = 9.81 m/s?.

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### Physics Problem: Pulley System with Two Blocks

In the given illustration, consider a system with two blocks connected by a cord passing over a pulley, where:

- Block 1 has a mass \( m_1 = 479 \, \text{g} \)
- Block 2 has a mass \( m_2 = 512 \, \text{g} \)
- The pulley has a radius \( R = 5.09 \, \text{cm} \) and is mounted on a frictionless horizontal axle

### Problem Description:
When released from rest, block 2 falls a distance of \( 77.6 \, \text{cm} \) in \( 5.13 \, \text{s} \) without the cord slipping on the pulley. This setup prompts several questions to solve:

1. **Acceleration of the Blocks (a)**: What is the magnitude of the acceleration of the blocks?
2. **Tension T2 (b)**: What is the tension \( T_2 \) (the tension force on block 2)?
3. **Tension T1 (c)**: What is the tension \( T_1 \) (the tension force on block 1)?
4. **Pulley’s Angular Acceleration (d)**: What is the magnitude of the pulley's angular acceleration?
5. **Rotational Inertia (e)**: What is the rotational inertia of the pulley?

Use the gravitational constant \( g = 9.81 \, \text{m/s}^2 \).

### Diagram Explanation:
The illustration depicts a pulley system with:
- Block 1 (mass \( m_1 \)) ascending
- Block 2 (mass \( m_2 \)) descending
- A fixed pulley rotating without friction, ensuring the cord does not slip

### Solution Boxes:
To provide the solutions to the questions, input the numerical values for:

(a) Magnitude of the blocks' acceleration.

(b) Tension \( T_2 \) in Newtons acting on block 2.

(c) Tension \( T_1 \) in Newtons acting on block 1.

(d) Magnitude of the pulley's angular acceleration.

(e) Rotational inertia of the pulley.

All values must be calculated using the provided parameters, the laws of motion, and rotational dynamics. Please ensure accuracy to avoid rounding errors during intermediate steps.

---

- **(a)** Number [Input
Transcribed Image Text:### Physics Problem: Pulley System with Two Blocks In the given illustration, consider a system with two blocks connected by a cord passing over a pulley, where: - Block 1 has a mass \( m_1 = 479 \, \text{g} \) - Block 2 has a mass \( m_2 = 512 \, \text{g} \) - The pulley has a radius \( R = 5.09 \, \text{cm} \) and is mounted on a frictionless horizontal axle ### Problem Description: When released from rest, block 2 falls a distance of \( 77.6 \, \text{cm} \) in \( 5.13 \, \text{s} \) without the cord slipping on the pulley. This setup prompts several questions to solve: 1. **Acceleration of the Blocks (a)**: What is the magnitude of the acceleration of the blocks? 2. **Tension T2 (b)**: What is the tension \( T_2 \) (the tension force on block 2)? 3. **Tension T1 (c)**: What is the tension \( T_1 \) (the tension force on block 1)? 4. **Pulley’s Angular Acceleration (d)**: What is the magnitude of the pulley's angular acceleration? 5. **Rotational Inertia (e)**: What is the rotational inertia of the pulley? Use the gravitational constant \( g = 9.81 \, \text{m/s}^2 \). ### Diagram Explanation: The illustration depicts a pulley system with: - Block 1 (mass \( m_1 \)) ascending - Block 2 (mass \( m_2 \)) descending - A fixed pulley rotating without friction, ensuring the cord does not slip ### Solution Boxes: To provide the solutions to the questions, input the numerical values for: (a) Magnitude of the blocks' acceleration. (b) Tension \( T_2 \) in Newtons acting on block 2. (c) Tension \( T_1 \) in Newtons acting on block 1. (d) Magnitude of the pulley's angular acceleration. (e) Rotational inertia of the pulley. All values must be calculated using the provided parameters, the laws of motion, and rotational dynamics. Please ensure accuracy to avoid rounding errors during intermediate steps. --- - **(a)** Number [Input
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