2.17 For the wheelbarrow shown, find the moment of the 100 weight about the center of the wheel. Also, determine the force P required to resist this moment.
2.17 For the wheelbarrow shown, find the moment of the 100 weight about the center of the wheel. Also, determine the force P required to resist this moment.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Problem 2.17: Moment Calculation for a Wheelbarrow
**Problem Statement:**
For the wheelbarrow shown, find the moment of the 100-pound (100#) weight about the center of the wheel. Also, determine the force \( P \) required to resist this moment.
**Diagram Explanation:**
The given image illustrates a side view of a wheelbarrow loaded with a weight of 100 pounds. Key details from the diagram include:
- The wheelbarrow has two handles extending from the wheel axis.
- The weight (100#) is positioned vertically above a specific point on the wheelbarrow.
- The distance from the wheel (pivot point) to the point where the weight is applied is shown as 20 inches horizontally.
- There are two segments indicating other distances on the handles:
- 20 inches from the center of the wheel to the load application point.
- Additional 20 inches to the end of the wheelbarrow handles where force \( P \) is applied.
**Steps to Solve:**
1. **Calculate the Moment due to the Weight:**
- The moment \( M \) around the wheel’s center caused by the 100# weight can be calculated using the formula:
\[
M = \text{Force} \times \text{Distance}
\]
Here:
\[
M = 100 \text{ pounds} \times 20 \text{ inches}
\]
This gives:
\[
M = 2000 \text{ pound-inches}
\]
2. **Determine the Force \( P \) to Resist the Moment:**
- The resisting force \( P \) creates a counter-clockwise moment about the wheel’s center.
- The distance from the pivot point to where \( P \) acts is 40 inches (20 inches + 20 inches).
Using the moment equilibrium condition:
\[
P \times 40 \text{ inches} = 2000 \text{ pound-inches}
\]
Solving for \( P \):
\[
P = \frac{2000 \text{ pound-inches}}{40 \text{ inches}} = 50 \text{ pounds}
\]
**Conclusion:**
- The moment of the 100# weight about the center of the wheel is 2000 pound-inches.
- The force \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ec45086-8540-448a-8175-f3c58b1b51d8%2F841c87f5-7704-4eec-a67c-693597c65db4%2Fmma3ywm_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 2.17: Moment Calculation for a Wheelbarrow
**Problem Statement:**
For the wheelbarrow shown, find the moment of the 100-pound (100#) weight about the center of the wheel. Also, determine the force \( P \) required to resist this moment.
**Diagram Explanation:**
The given image illustrates a side view of a wheelbarrow loaded with a weight of 100 pounds. Key details from the diagram include:
- The wheelbarrow has two handles extending from the wheel axis.
- The weight (100#) is positioned vertically above a specific point on the wheelbarrow.
- The distance from the wheel (pivot point) to the point where the weight is applied is shown as 20 inches horizontally.
- There are two segments indicating other distances on the handles:
- 20 inches from the center of the wheel to the load application point.
- Additional 20 inches to the end of the wheelbarrow handles where force \( P \) is applied.
**Steps to Solve:**
1. **Calculate the Moment due to the Weight:**
- The moment \( M \) around the wheel’s center caused by the 100# weight can be calculated using the formula:
\[
M = \text{Force} \times \text{Distance}
\]
Here:
\[
M = 100 \text{ pounds} \times 20 \text{ inches}
\]
This gives:
\[
M = 2000 \text{ pound-inches}
\]
2. **Determine the Force \( P \) to Resist the Moment:**
- The resisting force \( P \) creates a counter-clockwise moment about the wheel’s center.
- The distance from the pivot point to where \( P \) acts is 40 inches (20 inches + 20 inches).
Using the moment equilibrium condition:
\[
P \times 40 \text{ inches} = 2000 \text{ pound-inches}
\]
Solving for \( P \):
\[
P = \frac{2000 \text{ pound-inches}}{40 \text{ inches}} = 50 \text{ pounds}
\]
**Conclusion:**
- The moment of the 100# weight about the center of the wheel is 2000 pound-inches.
- The force \(
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