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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Question

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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