Part G Write equations for the constraints and other given information in this problem, the fact that the length of the string does not change imposes a constraint on relative accelerations of the two blocks. Find a relationship between the x component of the acceleration of block 2, a2x, and the acceleration of block 1. Pay careful attention to signs. Express a2x in terms of aix and/or aly, the components of the acceleration vector of block 1. ► View Available Hint(s) a2x = [5] ΑΣΦ xa Xb b √x x x Submit Previous Answers Request Answer x |X| X.10n

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Part G**

**Write equations for the constraints and other given information:** In this problem, the fact that the length of the string does not change imposes a constraint on relative accelerations of the two blocks. Find a relationship between the x component of the acceleration of block 2, \( a_{2x} \), and the acceleration of block 1. Pay careful attention to signs.

**Express** \( a_{2x} \) **in terms of** \( a_{1x} \) **and/or** \( a_{1y} \), **the components of the acceleration vector of block 1.**

- \( a_{2x} = \) [Input box for answer]

- [Button] Submit
- [Link] Previous Answers
- [Link] Request Answer

A toolbar with symbols and mathematical notation is provided above the input box to assist in typing the equation.
Transcribed Image Text:**Part G** **Write equations for the constraints and other given information:** In this problem, the fact that the length of the string does not change imposes a constraint on relative accelerations of the two blocks. Find a relationship between the x component of the acceleration of block 2, \( a_{2x} \), and the acceleration of block 1. Pay careful attention to signs. **Express** \( a_{2x} \) **in terms of** \( a_{1x} \) **and/or** \( a_{1y} \), **the components of the acceleration vector of block 1.** - \( a_{2x} = \) [Input box for answer] - [Button] Submit - [Link] Previous Answers - [Link] Request Answer A toolbar with symbols and mathematical notation is provided above the input box to assist in typing the equation.
### Learning Goal:
When you decide to solve a problem using Newton's 2nd law, follow these steps for a structured solution:

- **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.**

#### Application Example:
To illustrate this procedure, consider finding the acceleration of a block of mass \( m_2 \) that is pulled up a frictionless plane inclined at an angle \( \theta \) with respect to the horizontal. This setup involves a massless string that passes over a massless, frictionless pulley to a block of mass \( m_1 \) that is hanging vertically.

### Figure:
- **Diagram Content:**
  - **Block 2**: Positioned on a slope inclined at angle \( \theta \).
  - **Block 1**: Suspended vertically.
  - **Inclined Plane**: Frictionless and angled.
  - **Pulley**: Massless and frictionless, guiding the string connecting the blocks. 

This visual representation helps to conceptualize the physical setup for analysis using Newton's 2nd law.
Transcribed Image Text:### Learning Goal: When you decide to solve a problem using Newton's 2nd law, follow these steps for a structured solution: - **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.** #### Application Example: To illustrate this procedure, consider finding the acceleration of a block of mass \( m_2 \) that is pulled up a frictionless plane inclined at an angle \( \theta \) with respect to the horizontal. This setup involves a massless string that passes over a massless, frictionless pulley to a block of mass \( m_1 \) that is hanging vertically. ### Figure: - **Diagram Content:** - **Block 2**: Positioned on a slope inclined at angle \( \theta \). - **Block 1**: Suspended vertically. - **Inclined Plane**: Frictionless and angled. - **Pulley**: Massless and frictionless, guiding the string connecting the blocks. This visual representation helps to conceptualize the physical setup for analysis using Newton's 2nd law.
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