A particle subject to a force F(x, y) = (-6y, 6x) moves clockwise along the arc of a circle of radius 4 centered at the origin, beginning at (0, 4) and ending at (4,0). (a) Find the work done by F. Be sure you can explain the sign of your answer. Work = (b) How much work is done if the particle moves from (0, 4) to (4,0) along the circular arc as before, then in a straight line to the origin, and then in a straight line to (0, 4)? Hint: Sketch this closed path and the vector field. Work = (c) Is F path-independent? ? Be sure you can explain your answer.
A particle subject to a force F(x, y) = (-6y, 6x) moves clockwise along the arc of a circle of radius 4 centered at the origin, beginning at (0, 4) and ending at (4,0). (a) Find the work done by F. Be sure you can explain the sign of your answer. Work = (b) How much work is done if the particle moves from (0, 4) to (4,0) along the circular arc as before, then in a straight line to the origin, and then in a straight line to (0, 4)? Hint: Sketch this closed path and the vector field. Work = (c) Is F path-independent? ? Be sure you can explain your answer.
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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The answer is not 3pi or -3pi and I am struggling to find out what it is please help
Transcribed Image Text:A particle subject to a force F(x, y) = (-6y, 6x) moves clockwise along the arc of a circle of radius 4 centered at the origin, beginning at (0,4) and ending at (4,0).
(a) Find the work done by F. Be sure you can explain the sign of your answer.
Work =
(b) How much work is done if the particle moves from (0,4) to (4,0) along the circular arc as before, then in a straight line to the origin, and then in a straight line to (0,4)? Hint: Sketch this closed path and
the vector field.
Work =
(c) IsF path-independent? ?
✓ Be sure you can explain your answer.
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