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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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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?
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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