### Problem DescriptionThe motor turns gear A with a constant angular acceleration, \(\alpha = 4 \, \text{rad/s}^2\), starting from rest.Given:- Radius of gear A, \(r_A = 71 \, \text{mm}\)- Radius of gear B, \(r_B = 230 \, \text{mm}\)- Radius of pulley D, \(r_D = 121 \, \text{mm}\)The cord is wrapped around pulley D, which is rigidly attached to gear B.### Diagram ExplanationThe provided diagram shows:- Gear A on the left with a radius \(r_A\)- Gear B on the right with a larger radius \(r_B\)- Pulley D, which is rigidly attached to gear B, with radius \(r_D\)- A cord wrapped around pulley D- A cylinder C hanging from the cord### ProblemFind the distance (in mm) that cylinder C travels after \(t = 2.4 \, \text{seconds}\). Provide the answer as an integer.### SolutionTo find the distance, we need to calculate the linear displacement of the cord, which will be equal to the linear distance the cylinder C travels.1. **Angular Displacement Calculation for Gear A:** - Gear A has a constant angular acceleration and starts from rest. - Use the formula for angular displacement: \[ \theta_A = \frac{1}{2} \alpha t^2 \] Given \(\alpha_A = 4 \, \text{rad/s}^2\) and \(t = 2.4 \, \text{s}\): \[ \theta_A = \frac{1}{2} \times 4 \times (2.4)^2 \] \[ \theta_A = \frac{1}{2} \times 4 \times 5.76 \] \[ \theta_A = 11.52 \, \text{rad} \]2. **Angular Velocity Relation Between Gears:** - Gears A and B are meshed, hence their tangential velocities are equal: \[ r_A \omega_A = r_B \omega_B \] Since \(\omega\) is proportional to \(\theta

The distance of cylinder C.Given:The angular acceleration of the gear .The radius of the gear .The…

The motor turns gear A with a constant angular acceleration, a=4 rad/s², starting from rest. TA=71, rB=230, rD=121 The cord is wrapped around pulley D which is rigidly attached to gear B. LA TA D тав Find the distance of cylinder C in mm that it travels it t=2.4 sec. Give your answer as an integer.

The motor turns gear A with a constant angular acceleration, a=4 rad/s², starting from rest. TA=71, rB=230, rD=121 The cord is wrapped around pulley D which is rigidly attached to gear B. LA TA D тав Find the distance of cylinder C in mm that it travels it t=2.4 sec. Give your answer as an integer.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Problem Description

The motor turns gear A with a constant angular acceleration, \(\alpha = 4 \, \text{rad/s}^2\), starting from rest.

Given:
- Radius of gear A, \(r_A = 71 \, \text{mm}\)
- Radius of gear B, \(r_B = 230 \, \text{mm}\)
- Radius of pulley D, \(r_D = 121 \, \text{mm}\)

The cord is wrapped around pulley D, which is rigidly attached to gear B.

### Diagram Explanation

The provided diagram shows:
- Gear A on the left with a radius \(r_A\)
- Gear B on the right with a larger radius \(r_B\)
- Pulley D, which is rigidly attached to gear B, with radius \(r_D\)
- A cord wrapped around pulley D
- A cylinder C hanging from the cord

### Problem

Find the distance (in mm) that cylinder C travels after \(t = 2.4 \, \text{seconds}\). Provide the answer as an integer.

### Solution

To find the distance, we need to calculate the linear displacement of the cord, which will be equal to the linear distance the cylinder C travels.

1. **Angular Displacement Calculation for Gear A:**
- Gear A has a constant angular acceleration and starts from rest.
- Use the formula for angular displacement:
\[
\theta_A = \frac{1}{2} \alpha t^2
\]
Given \(\alpha_A = 4 \, \text{rad/s}^2\) and \(t = 2.4 \, \text{s}\):
\[
\theta_A = \frac{1}{2} \times 4 \times (2.4)^2
\]
\[
\theta_A = \frac{1}{2} \times 4 \times 5.76
\]
\[
\theta_A = 11.52 \, \text{rad}
\]

2. **Angular Velocity Relation Between Gears:**
- Gears A and B are meshed, hence their tangential velocities are equal:
\[
r_A \omega_A = r_B \omega_B
\]
Since \(\omega\) is proportional to \(\theta

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