College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Learning Goal:**
The blocks shown in Figure 1, connected by a short cable, are initially at rest. A force \( F = 300 \, \text{N} \) directed up the incline is applied and the blocks accelerate up the ramp. The coefficient of kinetic friction between the blocks and the ramp is \( \mu_k = 0.17 \), and the masses are \( m_A = 13 \, \text{kg} \) and \( m_B = 24 \, \text{kg} \). The angle of the incline is \( \theta = 20^\circ \). How long does it take for the blocks to reach \( v = 2 \, \text{m/s} \)? What is the tension in the cable between the blocks?
**Figure:**
The diagram depicts a block on an inclined plane. Several forces are labeled:
- \( F \), the applied force, directed up the incline.
- \( F_f \), the frictional force, opposing the motion.
- \( W \), the weight of the block, acting vertically downward.
- \( N \), the normal force, perpendicular to the surface.
**Part C:**
What is the magnitude of the acceleration of the blocks?
*Express your answer to three significant figures with appropriate units.*
- \( a_x = \) [ Value ] [ Units ] \[ \boxed{\phantom{\sum}} \]
**Part D:**
How long does it take for the blocks to reach \( v = 2 \, \text{m/s} \)?
*Express your answer to three significant figures with appropriate units.*
- \[ \boxed{\phantom{\sum}} \]
**Hints Available**: Viewing available hints is suggested.](https://content.bartleby.com/qna-images/question/858aa5e1-ece8-4a67-a0a4-477ec4c5e9a9/e2c0fe28-5cdb-4024-9dd0-74a03c01d2a7/tf1i9j_processed.jpeg)
Transcribed Image Text:**Learning Goal:**
The blocks shown in Figure 1, connected by a short cable, are initially at rest. A force \( F = 300 \, \text{N} \) directed up the incline is applied and the blocks accelerate up the ramp. The coefficient of kinetic friction between the blocks and the ramp is \( \mu_k = 0.17 \), and the masses are \( m_A = 13 \, \text{kg} \) and \( m_B = 24 \, \text{kg} \). The angle of the incline is \( \theta = 20^\circ \). How long does it take for the blocks to reach \( v = 2 \, \text{m/s} \)? What is the tension in the cable between the blocks?
**Figure:**
The diagram depicts a block on an inclined plane. Several forces are labeled:
- \( F \), the applied force, directed up the incline.
- \( F_f \), the frictional force, opposing the motion.
- \( W \), the weight of the block, acting vertically downward.
- \( N \), the normal force, perpendicular to the surface.
**Part C:**
What is the magnitude of the acceleration of the blocks?
*Express your answer to three significant figures with appropriate units.*
- \( a_x = \) [ Value ] [ Units ] \[ \boxed{\phantom{\sum}} \]
**Part D:**
How long does it take for the blocks to reach \( v = 2 \, \text{m/s} \)?
*Express your answer to three significant figures with appropriate units.*
- \[ \boxed{\phantom{\sum}} \]
**Hints Available**: Viewing available hints is suggested.
![**Educational Content: Dynamics and Inclines**
**Learning Goal:**
Understand the dynamics of blocks connected by a cable on an incline under the influence of an external force.
**Problem Description:**
The blocks shown in the figure are connected by a short cable and start at rest. A force \( F = 300 \, \text{N} \) is applied up the incline, causing the blocks to accelerate. The coefficient of kinetic friction between the blocks and the ramp is \( \mu_k = 0.17 \). The masses are \( m_A = 13 \, \text{kg} \) and \( m_B = 24 \, \text{kg} \). The angle of the incline is \( \theta = 20^\circ \).
**Key Questions:**
1. How long does it take for the blocks to reach \( v = 2 \, \text{m/s} \)?
2. What is the tension in the cable between the blocks?
**Part A:**
Consider the two blocks as a single system on the incline (as per Figure 2). Write the equation of motion using Newton’s second law for the blocks parallel to the surface. Include the force of friction \( F_{\text{fr}} \), the combined weight \( W \) of the blocks, and the applied force \( F \). Assume up the incline is positive.
**Equation to Determine:**
Express your answer in terms of \( F_{\text{fr}}, W, F, \) and \( \theta \).
\[ (m_A + m_B) a_x = \]
**Part B:**
Determine the magnitude of the friction force opposing the motion of the blocks up the ramp.
**Instructions:**
Express your answer with three significant figures and include appropriate units.
**Diagram Explanation:**
The figure illustrates two blocks, A and B, on an inclined plane with a force \( F \) applied parallel to the incline. Mass A is closer to the force application point. The incline angle is \( \theta = 20^\circ \).
**Physical Concepts:**
- Newton's Second Law for a system
- Components of gravitational force on an incline
- Kinetic friction and its role in motion on an inclined plane
**Calculation Approach:**
- Decompose forces parallel and perpendicular to the incline
- Use trigonometry to relate forces with the incline angle
- Solve for acceleration and tension using dynamics equations
**Practical](https://content.bartleby.com/qna-images/question/858aa5e1-ece8-4a67-a0a4-477ec4c5e9a9/e2c0fe28-5cdb-4024-9dd0-74a03c01d2a7/s2hkd5_processed.jpeg)
Transcribed Image Text:**Educational Content: Dynamics and Inclines**
**Learning Goal:**
Understand the dynamics of blocks connected by a cable on an incline under the influence of an external force.
**Problem Description:**
The blocks shown in the figure are connected by a short cable and start at rest. A force \( F = 300 \, \text{N} \) is applied up the incline, causing the blocks to accelerate. The coefficient of kinetic friction between the blocks and the ramp is \( \mu_k = 0.17 \). The masses are \( m_A = 13 \, \text{kg} \) and \( m_B = 24 \, \text{kg} \). The angle of the incline is \( \theta = 20^\circ \).
**Key Questions:**
1. How long does it take for the blocks to reach \( v = 2 \, \text{m/s} \)?
2. What is the tension in the cable between the blocks?
**Part A:**
Consider the two blocks as a single system on the incline (as per Figure 2). Write the equation of motion using Newton’s second law for the blocks parallel to the surface. Include the force of friction \( F_{\text{fr}} \), the combined weight \( W \) of the blocks, and the applied force \( F \). Assume up the incline is positive.
**Equation to Determine:**
Express your answer in terms of \( F_{\text{fr}}, W, F, \) and \( \theta \).
\[ (m_A + m_B) a_x = \]
**Part B:**
Determine the magnitude of the friction force opposing the motion of the blocks up the ramp.
**Instructions:**
Express your answer with three significant figures and include appropriate units.
**Diagram Explanation:**
The figure illustrates two blocks, A and B, on an inclined plane with a force \( F \) applied parallel to the incline. Mass A is closer to the force application point. The incline angle is \( \theta = 20^\circ \).
**Physical Concepts:**
- Newton's Second Law for a system
- Components of gravitational force on an incline
- Kinetic friction and its role in motion on an inclined plane
**Calculation Approach:**
- Decompose forces parallel and perpendicular to the incline
- Use trigonometry to relate forces with the incline angle
- Solve for acceleration and tension using dynamics equations
**Practical
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