Weight = 6 Ду. %3D Suppose it is at a vertical distance y from the winding engine, then Distance moved = A 15 - y) ft. Step 4 Now, the work done, W2, in winding up 15 ft of cable is 6(15 - у) dy %3D [15y- Y %3D ft-lb. %3D
Weight = 6 Ду. %3D Suppose it is at a vertical distance y from the winding engine, then Distance moved = A 15 - y) ft. Step 4 Now, the work done, W2, in winding up 15 ft of cable is 6(15 - у) dy %3D [15y- Y %3D ft-lb. %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![Consider a denolition crane with a 35-pound ball suspended from a 40-foot cable that weighs 6 pounds per foot.
Exercise (a)
Find the work required to wind up 15 feet of the apparatus.
Step 1
Note that in the current situation, as the cable is pulled, the following things happen.
1. The ball gets lifted with a constant
constant force.
2. The cable that is wound up gets lifted with a variable variable force.
3. The cable that doesn't get wound up is lifted with a constant
constant force.
Step 2
Calculate the work done, W,, in pulling up the ball while winding up 15 ft of the apparatus.
W, = force x distance = 35 x 15 = 525
525 ft-lb
Step 3
Consider an elemental length Ay, of the cable that gets wound up. As the cable weighs 6 pounds per feet:
Weight = 6
Ay.
Suppose it is at a vertical distance y from the winding engine, then
Distance moved = (6
15 -) ft.
a
e Type here to search](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F798cda9d-ac17-48ac-ac7e-2cc90951d035%2Ff4423037-4d95-4c31-abb8-29bc7cfbf109%2F9oev8th_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a denolition crane with a 35-pound ball suspended from a 40-foot cable that weighs 6 pounds per foot.
Exercise (a)
Find the work required to wind up 15 feet of the apparatus.
Step 1
Note that in the current situation, as the cable is pulled, the following things happen.
1. The ball gets lifted with a constant
constant force.
2. The cable that is wound up gets lifted with a variable variable force.
3. The cable that doesn't get wound up is lifted with a constant
constant force.
Step 2
Calculate the work done, W,, in pulling up the ball while winding up 15 ft of the apparatus.
W, = force x distance = 35 x 15 = 525
525 ft-lb
Step 3
Consider an elemental length Ay, of the cable that gets wound up. As the cable weighs 6 pounds per feet:
Weight = 6
Ay.
Suppose it is at a vertical distance y from the winding engine, then
Distance moved = (6
15 -) ft.
a
e Type here to search
![weighs 6 pounds per feet:
Weight =
6 Ду.
Suppose it is at a vertical distance y from the winding engine, then
Distance moved =
A 15 - y) ft.
Step 4
Now, the work done, W,, in winding up 15 ft of cable is
W2 =
6(15 - y) dy
[15y-
6.
ft-lb.
Submit
Skip (you cannot come back)
Exercise (b)
Find the work required to wind up all 40 feet of the apparatus.
Click here to begin!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F798cda9d-ac17-48ac-ac7e-2cc90951d035%2Ff4423037-4d95-4c31-abb8-29bc7cfbf109%2F1k1fdw9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:weighs 6 pounds per feet:
Weight =
6 Ду.
Suppose it is at a vertical distance y from the winding engine, then
Distance moved =
A 15 - y) ft.
Step 4
Now, the work done, W,, in winding up 15 ft of cable is
W2 =
6(15 - y) dy
[15y-
6.
ft-lb.
Submit
Skip (you cannot come back)
Exercise (b)
Find the work required to wind up all 40 feet of the apparatus.
Click here to begin!
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.
Step by step
Solved in 4 steps
![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, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning