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...
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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.
Transcribed Image Text: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
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