### Problem StatementGear \( A \) has an initial angular velocity of 60 rad/sec and a constant angular deceleration of 1.2 rad/sec\(^2\). When \( t = 3 \) sec, calculate the magnitude of deceleration of the block hoisted by the hub on gear \( B \). Present your answer in ft/sec\(^2\) using 3 significant figures.### Diagram ExplanationThe diagram shows two gears, \( A \) and \( B \). Gear \( A \) has a radius of 1 ft. It is meshed with gear \( B \), which has a larger radius of 2 ft. There is a rope wound around a smaller hub with a radius of 0.5 ft on gear \( B \), which lifts a block as gear \( B \) rotates. The illustration depicts gear \( A \) rotating clockwise, which in turn affects the motion of gear \( B \).### Solution Steps1. **Determine the angular velocity of Gear B:** - Gear ratio between gears \( A \) and \( B \): \( \frac{r_A}{r_B} = \frac{1}{2} \). - Angular velocity of gear \( B \) is half of that of gear \( A \).2. **Calculate the linear velocity of the block:** - Using the radius of the hub on gear \( B \).3. **Calculate the angular deceleration of Gear B:** - Reduce by the same gear ratio.4. **Calculate the deceleration of the block:** - Using the linear relationship with the hub radius.This process will yield the deceleration in ft/sec\(^2\) rounded to three significant figures, as required.

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Gear A has an initial angular velocity of 60 rad/sec and a constant angular deceleration of 1.2 rad/sec². When t = 3 sec, calculate the magnitude of deceleration of the block hoisted by the hub on gear B. Present your answer in ft/sec² using 3 significant figures.

Gear A has an initial angular velocity of 60 rad/sec and a constant angular deceleration of 1.2 rad/sec². When t = 3 sec, calculate the magnitude of deceleration of the block hoisted by the hub on gear B. Present your answer in ft/sec² using 3 significant figures.

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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Concept explainers

Power Transmission Elements

It is defined as the energy transfer from one location to another location. The energy will start moving from the energy generation source to the energy applied position to obtain the work output. From this method, a large amount of electric energy moves from the power station to various electrical substations.

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### Problem Statement

Gear \( A \) has an initial angular velocity of 60 rad/sec and a constant angular deceleration of 1.2 rad/sec\(^2\). When \( t = 3 \) sec, calculate the magnitude of deceleration of the block hoisted by the hub on gear \( B \). Present your answer in ft/sec\(^2\) using 3 significant figures.

### Diagram Explanation

The diagram shows two gears, \( A \) and \( B \). Gear \( A \) has a radius of 1 ft. It is meshed with gear \( B \), which has a larger radius of 2 ft. There is a rope wound around a smaller hub with a radius of 0.5 ft on gear \( B \), which lifts a block as gear \( B \) rotates. The illustration depicts gear \( A \) rotating clockwise, which in turn affects the motion of gear \( B \).

### Solution Steps

1. **Determine the angular velocity of Gear B:**
- Gear ratio between gears \( A \) and \( B \): \( \frac{r_A}{r_B} = \frac{1}{2} \).
- Angular velocity of gear \( B \) is half of that of gear \( A \).

2. **Calculate the linear velocity of the block:**
- Using the radius of the hub on gear \( B \).

3. **Calculate the angular deceleration of Gear B:**
- Reduce by the same gear ratio.

4. **Calculate the deceleration of the block:**
- Using the linear relationship with the hub radius.

This process will yield the deceleration in ft/sec\(^2\) rounded to three significant figures, as required.

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