Inverse force fields Consider the radial field (х, у, 2) where p > 1 (the inverse square law corresponds to p = 3). Let C be the line segment from (1, 1, 1) to (a, a, a), where a > 1, given by r(t) = (1, 1, t), for 1 sts a. a. Find the work done in moving an object along C with p = 2. b. If a→ * in part (a), is the work finite? c. Find the work done in moving an object along C with p = 4. d. If a → o in part (c), is the work finite? e. Find the work done in moving an object along C for any p > 1. f. If a→ * in part (e), for what values of p is the work finite?
Inverse force fields Consider the radial field (х, у, 2) where p > 1 (the inverse square law corresponds to p = 3). Let C be the line segment from (1, 1, 1) to (a, a, a), where a > 1, given by r(t) = (1, 1, t), for 1 sts a. a. Find the work done in moving an object along C with p = 2. b. If a→ * in part (a), is the work finite? c. Find the work done in moving an object along C with p = 4. d. If a → o in part (c), is the work finite? e. Find the work done in moving an object along C for any p > 1. f. If a→ * in part (e), for what values of p is the work finite?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 31E
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Question
![Inverse force fields Consider the radial field
(х, у, 2)
where p > 1 (the inverse square law
corresponds to p = 3). Let C be the line segment from (1, 1, 1) to
(a, a, a), where a > 1, given by r(t) = (1, 1, t), for 1 sts a.
a. Find the work done in moving an object along C with p = 2.
b. If a→ * in part (a), is the work finite?
c. Find the work done in moving an object along C with p = 4.
d. If a → o in part (c), is the work finite?
e. Find the work done in moving an object along C for any
p > 1.
f. If a→ * in part (e), for what values of p is the work finite?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc655501b-78fb-4dca-99a6-6372bd9dd726%2Fb99f98c7-df3b-400c-902b-93611ff5ca6d%2F1pd2xxr.png&w=3840&q=75)
Transcribed Image Text:Inverse force fields Consider the radial field
(х, у, 2)
where p > 1 (the inverse square law
corresponds to p = 3). Let C be the line segment from (1, 1, 1) to
(a, a, a), where a > 1, given by r(t) = (1, 1, t), for 1 sts a.
a. Find the work done in moving an object along C with p = 2.
b. If a→ * in part (a), is the work finite?
c. Find the work done in moving an object along C with p = 4.
d. If a → o in part (c), is the work finite?
e. Find the work done in moving an object along C for any
p > 1.
f. If a→ * in part (e), for what values of p is the work finite?
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