Show that / F dr is independent of its path, given that F(r, y, :) = + tan-:) i+tan rj+ k. IHence, find the potential function of Fand then evaluate the work done by F moving an object along the smooth curve C, the line segment from (1,0.-1) to (0.0.0) then along the parabola z= y,ar = 0 to (0.-1. 1).
Show that / F dr is independent of its path, given that F(r, y, :) = + tan-:) i+tan rj+ k. IHence, find the potential function of Fand then evaluate the work done by F moving an object along the smooth curve C, the line segment from (1,0.-1) to (0.0.0) then along the parabola z= y,ar = 0 to (0.-1. 1).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 62E
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![b) Show that
F dr is independent of its path, given that
F(r, y, 2) = (
+ tan-:) i+ tan rj+
k.
1+:2
1+
IHence, find the potential function of Fand then evaluate the work done
by Fmoving an object along the smooth curve C, the line segment from
(1,0,–1) to (0.0.0) then along the parabola 3 = y, r = 0 to (0.-1. 1).
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c101dd0-25cf-4b0b-b18c-63e93a3d7ec6%2F01fa8ae9-0e21-4f9c-9ac9-d7a7ed119050%2F15oa59_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b) Show that
F dr is independent of its path, given that
F(r, y, 2) = (
+ tan-:) i+ tan rj+
k.
1+:2
1+
IHence, find the potential function of Fand then evaluate the work done
by Fmoving an object along the smooth curve C, the line segment from
(1,0,–1) to (0.0.0) then along the parabola 3 = y, r = 0 to (0.-1. 1).
%3D
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