1.) Assume that some ancient civilization built their monuments with a compound system of simple machines. Given a system like this: P2 P1 1000 kg di dr FR di (TOTAL) If the efficiency of the incline plane (due to friction) is e, = 0.9, the efficiency of the first pulley (P1) is e = 0.8, the second pulley (P2) is ez = 0.7 dr = 5 m, and di = 20 m,
1.) Assume that some ancient civilization built their monuments with a compound system of simple machines. Given a system like this: P2 P1 1000 kg di dr FR di (TOTAL) If the efficiency of the incline plane (due to friction) is e, = 0.9, the efficiency of the first pulley (P1) is e = 0.8, the second pulley (P2) is ez = 0.7 dr = 5 m, and di = 20 m,
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
Related questions
Question
![### Simple Machine System for Building Monuments
1. **Concept Overview**: Imagine an ancient civilization using a compound system of simple machines to construct their monuments. The system includes an inclined plane and a series of pulleys to move a heavy block weighing 1000 kg.
2. **Diagram Explanation**:
- **Inclined Plane**: A sloped surface where the block is placed. The mechanical advantage helps in moving the block upwards.
- **Pulley System**: Two pulleys are used—P1 and P2. These pulleys assist in reducing the amount of input force needed to lift the block.
- **Force Directions**:
- \( F_R \) indicates the force exerted due to the block’s weight on the inclined plane.
- \( F_I \) is the input force applied, depicted with an arrow pulling horizontally.
- **Distance Labels**:
- \( d_i \): Distance along the inclined plane.
- \( d_R \): Vertical rise needed.
- \( d_{I(TOTAL)} \): Total horizontal distance over which the input force acts.
3. **Efficiency Parameters**:
- **Inclined Plane Efficiency (\( e_0 \))**: 0.9, accounting for friction.
- **Pulley Efficiencies**:
- First Pulley (P1) Efficiency (\( e_1 \)): 0.8
- Second Pulley (P2) Efficiency (\( e_2 \)): 0.7
4. **Distances**:
- \( d_R = 5 \, m \), the required vertical rise.
- \( d_i = 20 \, m \), the length of the incline.
This setup demonstrates how simple machines reduce the effort needed to perform work, a principle utilized in ancient engineering feats.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F203496de-9811-4b54-9c68-20804c67def9%2Fcefd4cdd-268d-4e12-bf19-3b9262601644%2Fhzh1ysp_processed.png&w=3840&q=75)
Transcribed Image Text:### Simple Machine System for Building Monuments
1. **Concept Overview**: Imagine an ancient civilization using a compound system of simple machines to construct their monuments. The system includes an inclined plane and a series of pulleys to move a heavy block weighing 1000 kg.
2. **Diagram Explanation**:
- **Inclined Plane**: A sloped surface where the block is placed. The mechanical advantage helps in moving the block upwards.
- **Pulley System**: Two pulleys are used—P1 and P2. These pulleys assist in reducing the amount of input force needed to lift the block.
- **Force Directions**:
- \( F_R \) indicates the force exerted due to the block’s weight on the inclined plane.
- \( F_I \) is the input force applied, depicted with an arrow pulling horizontally.
- **Distance Labels**:
- \( d_i \): Distance along the inclined plane.
- \( d_R \): Vertical rise needed.
- \( d_{I(TOTAL)} \): Total horizontal distance over which the input force acts.
3. **Efficiency Parameters**:
- **Inclined Plane Efficiency (\( e_0 \))**: 0.9, accounting for friction.
- **Pulley Efficiencies**:
- First Pulley (P1) Efficiency (\( e_1 \)): 0.8
- Second Pulley (P2) Efficiency (\( e_2 \)): 0.7
4. **Distances**:
- \( d_R = 5 \, m \), the required vertical rise.
- \( d_i = 20 \, m \), the length of the incline.
This setup demonstrates how simple machines reduce the effort needed to perform work, a principle utilized in ancient engineering feats.
![3.) Assuming that the resistance distance for the total system is just the vertical displacement of the block \(d_R\), and the input distance for the total system is the distance the team of horses must pull \((d_{i(TOTAL)})\),
a. How far must the horses pull \((d_{i(TOTAL)})\) in order to raise the block the required 5 meters?
b. How much work is done by the horses?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F203496de-9811-4b54-9c68-20804c67def9%2Fcefd4cdd-268d-4e12-bf19-3b9262601644%2F9cifgp_processed.png&w=3840&q=75)
Transcribed Image Text:3.) Assuming that the resistance distance for the total system is just the vertical displacement of the block \(d_R\), and the input distance for the total system is the distance the team of horses must pull \((d_{i(TOTAL)})\),
a. How far must the horses pull \((d_{i(TOTAL)})\) in order to raise the block the required 5 meters?
b. How much work is done by the horses?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Control Systems Engineering](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
![Mechanics of Materials (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
![Engineering Mechanics: Statics](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY