(7) Consider a particle that moves going from the point (-2, 2) to the point (-2, 2) along the piecewise-linear path C depicted below: (-3,2) This particle is subject to a force field given by C 2x+y F(r,y)- (3) (a) You can use WolframAlpha to check that the (scalar) curl of Fis 0 on R² - {0). However. because R² - {0} is not a very nice set, we can't guarantee that F is conservative. In fact, show that there exists no scalar function g such that F Vg.
(7) Consider a particle that moves going from the point (-2, 2) to the point (-2, 2) along the piecewise-linear path C depicted below: (-3,2) This particle is subject to a force field given by C 2x+y F(r,y)- (3) (a) You can use WolframAlpha to check that the (scalar) curl of Fis 0 on R² - {0). However. because R² - {0} is not a very nice set, we can't guarantee that F is conservative. In fact, show that there exists no scalar function g such that F Vg.
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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Transcribed Image Text:(7) Consider a particle that moves going from the point (-2, 2) to the point (-2, 2) along the
piecewise-linear path C depicted below:
(-3,2)
(-2,-2)
This particle is subject to a force field given by
F(x, y) F
2x+y
2y - 2
2² +3² 2² +2²
(a) You can use WolframAlpha to check that the (scalar) curl of Fis 0 on R² - {0}. However,
because R²- {0} is not a very nice set, we can't guarantee that F is conservative. In fact, show
that there exists no scalar function g such that F= Vg.
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