Question 4(15 points): If the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lb, how much work is needed to stretch it 9 inches beyond its natural length? Solution: Choose the following coordinate system and let f(x) be the force function. Fixed wwwww Fixed Natural length f(x)=kx x feet By the Hooke's law, the force function has the form of f(x) =kx, where x is the amount stretched. The work required to stretch the spring 1 ft beyond its natural length is 12 ft-lb gives the following equation: f(x)dx=12 fkx dx = 12 => = 12 ⇒> k = 24 So the spring constant k = 24. Hence f(x)=24x. The work required = √9/1224xdx 6 points 3 points = 24x. = 12x리 27 = 12 × () = ft-lb 6 points
Question 4(15 points): If the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lb, how much work is needed to stretch it 9 inches beyond its natural length? Solution: Choose the following coordinate system and let f(x) be the force function. Fixed wwwww Fixed Natural length f(x)=kx x feet By the Hooke's law, the force function has the form of f(x) =kx, where x is the amount stretched. The work required to stretch the spring 1 ft beyond its natural length is 12 ft-lb gives the following equation: f(x)dx=12 fkx dx = 12 => = 12 ⇒> k = 24 So the spring constant k = 24. Hence f(x)=24x. The work required = √9/1224xdx 6 points 3 points = 24x. = 12x리 27 = 12 × () = ft-lb 6 points
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
Question
I am studying for a test I have tomorrow, this is one of the example problems that will be one the test, can you show the equations used in this problem answer and then explain. Can you also show how to make the graph and how changing something in the question will effected it as an example.
Expert Solution
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 2 steps with 4 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning