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Problem 1 The 2 blocks are originally at rest. The pulleys are smooth. The coefficient of friction between the block A and the incline are µg -0.25 and #x=0.2. The mass of the blocks are m- 100kg and Mg -200kg and the angle of the slope a = 20°. Ja 1. Find the relation between the acceleration of the block A and the block B 2. Do FBD and kinetic diagram of both blocks. 3. Solve for both accelerations, what is the direction of the motion? 4. Find the tension in the cable.

Problem 1 The 2 blocks are originally at rest. The pulleys are smooth. The coefficient of friction between the block A and the incline are µg -0.25 and #x=0.2. The mass of the blocks are m- 100kg and Mg -200kg and the angle of the slope a = 20°. Ja 1. Find the relation between the acceleration of the block A and the block B 2. Do FBD and kinetic diagram of both blocks. 3. Solve for both accelerations, what is the direction of the motion? 4. Find the tension in the cable.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Problem 1 The two blocks are originally at rest. The pulleys are smooth. The coefficient of friction between block A and the incline are μₛ = 0.25 and μₖ = 0.2. The mass of the blocks are \( m_A = 100 \text{kg} \) and \( m_B = 200 \text{kg} \) and the angle of the slope \( \alpha = 20^\circ \). ![Diagram](block_diagram.png) - **Diagram Description**: The diagram shows block A resting on an inclined plane and connected via a pulley system to block B, which hangs vertically. Block A is inclined at an angle \( \alpha \) to the horizontal. #### Questions: 1. **Find the relation between the acceleration of block A and block B**. 2. **Do Free Body Diagram (FBD) and kinetic diagram of both blocks**. 3. **Solve for both accelerations, what is the direction of the motion?** 4. **Find the tension in the cable**. ### Detailed Explanations: 1. **Relation between Accelerations**: - Since the blocks are connected by a pulley, the accelerations of block A and block B are related. Let's denote the acceleration of block A by \( a_A \) and block B by \( a_B \). Because of the pulley system, if block B moves down by a distance \( d \), block A moves up the incline by the same distance \( d \). Therefore, \( a_A = a_B = a \). 2. **Free Body Diagram (FBD) and Kinetic Diagram**: - **Block A**: - Weight component along the incline: \( m_A \cdot g \cdot \sin(\alpha) \) - Normal force: \( N_A = m_A \cdot g \cdot \cos(\alpha) \) - Frictional force: \( f = \mu_k \cdot N_A \) - Tension in the cable: \( T \) - **Block B**: - Weight: \( m_B \cdot g \) - Tension in the cable: \( T \) 3. **Solve for Accelerations**: - By applying Newton’s second law to each block and solving the system of equations: - For Block A: \( T - m_A \
Transcribed Image Text:### Problem 1 The two blocks are originally at rest. The pulleys are smooth. The coefficient of friction between block A and the incline are μₛ = 0.25 and μₖ = 0.2. The mass of the blocks are \( m_A = 100 \text{kg} \) and \( m_B = 200 \text{kg} \) and the angle of the slope \( \alpha = 20^\circ \). ![Diagram](block_diagram.png) - **Diagram Description**: The diagram shows block A resting on an inclined plane and connected via a pulley system to block B, which hangs vertically. Block A is inclined at an angle \( \alpha \) to the horizontal. #### Questions: 1. **Find the relation between the acceleration of block A and block B**. 2. **Do Free Body Diagram (FBD) and kinetic diagram of both blocks**. 3. **Solve for both accelerations, what is the direction of the motion?** 4. **Find the tension in the cable**. ### Detailed Explanations: 1. **Relation between Accelerations**: - Since the blocks are connected by a pulley, the accelerations of block A and block B are related. Let's denote the acceleration of block A by \( a_A \) and block B by \( a_B \). Because of the pulley system, if block B moves down by a distance \( d \), block A moves up the incline by the same distance \( d \). Therefore, \( a_A = a_B = a \). 2. **Free Body Diagram (FBD) and Kinetic Diagram**: - **Block A**: - Weight component along the incline: \( m_A \cdot g \cdot \sin(\alpha) \) - Normal force: \( N_A = m_A \cdot g \cdot \cos(\alpha) \) - Frictional force: \( f = \mu_k \cdot N_A \) - Tension in the cable: \( T \) - **Block B**: - Weight: \( m_B \cdot g \) - Tension in the cable: \( T \) 3. **Solve for Accelerations**: - By applying Newton’s second law to each block and solving the system of equations: - For Block A: \( T - m_A \
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