College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Part G
Transcribed Image Text:The content presented is part of a physics problem related to the dynamics of a block system on an inclined plane. It explains how to find the acceleration of a block of mass \( m_2 \), which is pulled up a frictionless plane inclined at an angle \( \theta \) with respect to the horizontal by a massless string. This string passes over a massless, frictionless pulley to a block of mass \( m_1 \) that is hanging vertically.
### Figure 1 Description:
The figure is divided into four parts labeled a, b, c, and d. They represent different configurations or components of the block system:
- **Figure a**: Shows Block 1 with mass \( m_{1g} \) moving on the inclined plane.
- **Figure b**: Similar to Figure a, shows another Block 2 with mass \( m_{2g} \) on the inclined plane.
- **Figure c**: Depicts Block 1 being pulled by a tension \( T_{3} \) and influenced by the gravitational force \( m_{1g} \).
- **Figure d**: Shows Block 2 with similar forces as in Figure c but with slight variations in the directions and magnitudes.
### Problem Explanation:
**Part G**: The task is to write equations for the constraints and given information in this block system. The aim is to find a relationship between the x-component of the acceleration of Block 2, \( a_{2x} \), and the acceleration of Block 1. The problem notes that the constant length of the string imposes a constraint on the relative accelerations of the two blocks. It emphasizes careful attention to signs when expressing \( a_{2x} \) in terms of \( a_{1x} \) and/or \( a_{1y} \), which are components of the acceleration vector of Block 1.
Below, you are prompted to input \( a_{2x} \) using a given formula box.
### Additional Note:
To solve this problem, consider Newton's laws of motion, constraints imposed by the system geometry, and how forces like tension and gravity affect the motion of both blocks.
)
**Figure Explanation:**
The figure illustrates a scenario with two blocks connected by a string over a pulley.
- **Block 2** is on an inclined plane, angled at \( \theta \), indicating the slope relative to the horizontal.
- **Block 1** is hanging vertically on the other side of the pulley.
- The pulley is represented as massless and frictionless, meaning it does not add any additional forces or resistance to the system.
- The string connecting the two blocks is also considered massless.
This setup is used to analyze the dynamics of the system by applying Newton's 2nd law, focusing on the forces and acceleration involved.](https://content.bartleby.com/qna-images/question/f0fdd9be-9990-44a9-8005-60989cbb2f12/e7073e7a-f159-49ce-9c14-8f2cbd76872e/ztgups_processed.png)
Transcribed Image Text:**Learning Goal:**
Once you have decided to solve a problem using Newton's 2nd law, there are steps that will lead you to a solution. One such prescription is the following:
- Visualize the problem and identify special cases.
- Isolate each body and draw the forces acting on it.
- Choose a coordinate system for each body.
- Apply Newton’s 2nd law to each body.
- Write equations for the constraints and other given information.
- Solve the resulting equations symbolically.
- Check that your answer has the correct dimensions and satisfies special cases.
- If numbers are given in the problem, plug them in and check that the answer makes sense.
- Think about generalizations or simplifications of the problem.
As an example, we will apply this procedure to find the acceleration of a block of mass \( m_2 \) that is pulled up a frictionless plane inclined at angle \( \theta \) with respect to the horizontal by a massless string that passes over a massless, frictionless pulley to a block of mass \( m_1 \) that is hanging vertically. ([Figure 1](#))
**Figure Explanation:**
The figure illustrates a scenario with two blocks connected by a string over a pulley.
- **Block 2** is on an inclined plane, angled at \( \theta \), indicating the slope relative to the horizontal.
- **Block 1** is hanging vertically on the other side of the pulley.
- The pulley is represented as massless and frictionless, meaning it does not add any additional forces or resistance to the system.
- The string connecting the two blocks is also considered massless.
This setup is used to analyze the dynamics of the system by applying Newton's 2nd law, focusing on the forces and acceleration involved.
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Follow-up Question
Transcribed Image Text:### Problem Statement
Express \( a_{1y} \) in terms of some or all of the variables \( m_1, m_2, \theta, \) and \( g \).
### Interface Elements
- **View Available Hint(s):** Button to display any hints available to solve the problem.
- **Input Area**: An input box labeled \( a_{1y} = \) where you can enter your answer.
- **Toolbar Options:**
- Square root and absolute value symbol.
- Greek letters and symbols option.
- Undo and redo buttons for correcting input.
- Keyboard icon for virtual keyboard access.
- **Submit Button**: Click to submit your answer.
### How to Approach
- Analyze the relationship between the given variables \( m_1, m_2, \theta, \) and \( g \).
- Use physical laws or mathematical equations relevant to the context (possibly Newton's second law, trigonometry, etc.) to express \( a_{1y} \).
- Input your derived expression in the box provided and submit it.
### Additional Notes
Make sure to consider all possible influences of the provided variables on \( a_{1y} \) and check for any simplifications.
Solution
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Follow-up Questions
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Follow-up Question
Transcribed Image Text:### Problem Statement
Express \( a_{1y} \) in terms of some or all of the variables \( m_1, m_2, \theta, \) and \( g \).
### Interface Elements
- **View Available Hint(s):** Button to display any hints available to solve the problem.
- **Input Area**: An input box labeled \( a_{1y} = \) where you can enter your answer.
- **Toolbar Options:**
- Square root and absolute value symbol.
- Greek letters and symbols option.
- Undo and redo buttons for correcting input.
- Keyboard icon for virtual keyboard access.
- **Submit Button**: Click to submit your answer.
### How to Approach
- Analyze the relationship between the given variables \( m_1, m_2, \theta, \) and \( g \).
- Use physical laws or mathematical equations relevant to the context (possibly Newton's second law, trigonometry, etc.) to express \( a_{1y} \).
- Input your derived expression in the box provided and submit it.
### Additional Notes
Make sure to consider all possible influences of the provided variables on \( a_{1y} \) and check for any simplifications.
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