Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
6th Edition
ISBN: 9781524908102
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.4, Problem 31PS
To determine
To find: The work done using the Green’s theorem by the force filed
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Check out a sample textbook solutionStudents have asked these similar questions
Consider the force field and circle defined below.
F(x,y)=x2 i+xyj
x2 +y2 =36
(a) Find the work done by the force field on a particle that moves once around the circle oriented in the clockwise direction.
(b) Use a computer algebra system to graph the force field and circle on the same screen.
REFER TO IMAGE
(a) Calculate the flux of the vector field
F(x, y, z) = 3i – 9k through a sphere of radius 2
centered at the origin, oriented outward.
Flux =
(b) Calculate the flux of the vector field
F(x, y, z) = i − 2j+ 6k through a cube of side length
2 with sides parallel to the axes, oriented outward.
Flux =
Chapter 13 Solutions
Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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- = xi + yj through the surface S, which is the part of the surface z = 36 – (x² + y2) above the disk of radius 6 Compute the flux of the vector field F centered at the origin, oriented upward. flux =arrow_forwardBrazilian soccer star Marta has a penalty kick in the quarter-final match. She kicks the soccer ball from ground level with the (x, y)-coordinates (76, 21) on the soccer field shown in the figure and with initial velocity vo = 8i - 4j+23k ft/s. Assume an acceleration of 32 ft/s² due to gravity and that the goal net has a height of 8 ft and a total width of 24 ft. 105 ft 105 ft ri = rj = 165 ft rk = e 165 ft Determine the position function that gives the position of the ball t seconds after it is hit. (Use symbolic notation and fractions where needed.) r(t) = r(t)i + r(t)j +rk(t)k 12 12 Xarrow_forwardLet I be the flux of G = (4e³,9x³ex⁹, 0) through the upper hemisphere S of the unit sphere. (a) Find a vector field A such that curl(A) = G. (b) Calculate the circulation of A around as. (c) Compute I, the flux of G through S. (a) A = (b) √ A · ds = (c) I =arrow_forward
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