Problem 4.32 The figure shows a block (mass mA) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block (mass mB), which hangs vertically. Ignore friction and the masses of the pulley and cord. (Figure 1) Figure < 1 of 1 Submi Part C Determine the acceleration of the system. Express your answer in terms of mд, mB, and g. IVE ΑΣΦ S → C ? Request Answer Part D Determine the tension in the cord. Express your answer in terms of mд, mB, and g. a= Submit

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# Problem 4.32

## Problem Statement

The figure shows a block (mass \( m_A \)) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block (mass \( m_B \)), which hangs vertically. Ignore friction and the masses of the pulley and cord. 

### Figure: 
The figure illustrates a system where:
- Block \( m_A \) rests on a smooth horizontal surface.
- Block \( m_B \) hangs vertically off the edge connected to block \( m_A \) by a cord that passes over a pulley.

## Questions

### Part C
**Determine the acceleration of the system.**

Express your answer in terms of \( m_A \), \( m_B \), and \( g \).

\[ a = \boxed{} \]

---

### Part D
**Determine the tension in the cord.**

Express your answer in terms of \( m_A \), \( m_B \), and \( g \).

\[ T = \boxed{} \]

---

### Diagram Explanation:
The diagram depicts:
1. **Block \( m_A \)**: Placed on a horizontal surface.
2. **Block \( m_B \)**: Hanging vertically.
3. **Cord and Pulley System**: The cord connects the two blocks and runs over a pulley at the edge.

When the system is released, block \( m_B \) will accelerate downward, and block \( m_A \) will accelerate horizontally to the right. The tension in the cord and the acceleration of the blocks need to be determined using Newton’s second law and the constraints of the system. 

### Concepts:
1. **Newton's Second Law:** Apply \( F=ma \) to find the equations of motion for block \( m_A \) and block \( m_B \).
2. **System Constraints:** The acceleration of both blocks is the same in magnitude but in different directions.

The overall goal is to solve the system of equations to find the acceleration and tension in the cord.
Transcribed Image Text:# Problem 4.32 ## Problem Statement The figure shows a block (mass \( m_A \)) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block (mass \( m_B \)), which hangs vertically. Ignore friction and the masses of the pulley and cord. ### Figure: The figure illustrates a system where: - Block \( m_A \) rests on a smooth horizontal surface. - Block \( m_B \) hangs vertically off the edge connected to block \( m_A \) by a cord that passes over a pulley. ## Questions ### Part C **Determine the acceleration of the system.** Express your answer in terms of \( m_A \), \( m_B \), and \( g \). \[ a = \boxed{} \] --- ### Part D **Determine the tension in the cord.** Express your answer in terms of \( m_A \), \( m_B \), and \( g \). \[ T = \boxed{} \] --- ### Diagram Explanation: The diagram depicts: 1. **Block \( m_A \)**: Placed on a horizontal surface. 2. **Block \( m_B \)**: Hanging vertically. 3. **Cord and Pulley System**: The cord connects the two blocks and runs over a pulley at the edge. When the system is released, block \( m_B \) will accelerate downward, and block \( m_A \) will accelerate horizontally to the right. The tension in the cord and the acceleration of the blocks need to be determined using Newton’s second law and the constraints of the system. ### Concepts: 1. **Newton's Second Law:** Apply \( F=ma \) to find the equations of motion for block \( m_A \) and block \( m_B \). 2. **System Constraints:** The acceleration of both blocks is the same in magnitude but in different directions. The overall goal is to solve the system of equations to find the acceleration and tension in the cord.
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