Suppose that F is any force field and 7(t) is any constant path. Calculate SF.d7. γ Let y be the boundary of the square [0, 1]×[0, 1] parameterized in the coun- terclockwise direction, and broken into a concatenation of four straight line segments V1 * 2 * 3 * 4 as follows: ⚫ Y₁ is the line segment from (0,0) to (1,0) Y2 is the line segment form (1,0) to (1,1) 3 is the line segment from (1, 1) to (0, 1) 4 is the line segment from (0, 1) to (0,0) Answer the following questions about the force field F(x,y) = (x²- y², 2xy) (a) Compute the amount of work done by ♬ in moving a particle in the counterclockwise direction around the square [0, 1] × [0, 1] along the path from (0,0) and back to (0,0). (b) Is F conservative? (Hint: Can you think of another path from (0,0) to (0,0) whose work integral is easy to calculate?)
Suppose that F is any force field and 7(t) is any constant path. Calculate SF.d7. γ Let y be the boundary of the square [0, 1]×[0, 1] parameterized in the coun- terclockwise direction, and broken into a concatenation of four straight line segments V1 * 2 * 3 * 4 as follows: ⚫ Y₁ is the line segment from (0,0) to (1,0) Y2 is the line segment form (1,0) to (1,1) 3 is the line segment from (1, 1) to (0, 1) 4 is the line segment from (0, 1) to (0,0) Answer the following questions about the force field F(x,y) = (x²- y², 2xy) (a) Compute the amount of work done by ♬ in moving a particle in the counterclockwise direction around the square [0, 1] × [0, 1] along the path from (0,0) and back to (0,0). (b) Is F conservative? (Hint: Can you think of another path from (0,0) to (0,0) whose work integral is easy to calculate?)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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![Suppose that F is any force field and 7(t) is any constant path. Calculate
SF.d7.
γ
Let y be the boundary of the square [0, 1]×[0, 1] parameterized in the coun-
terclockwise direction, and broken into a concatenation of four straight line
segments V1 * 2 * 3 * 4 as follows:
⚫ Y₁ is the line segment from (0,0) to (1,0)
Y2 is the line segment form (1,0) to (1,1)
3 is the line segment from (1, 1) to (0, 1)
4 is the line segment from (0, 1) to (0,0)
Answer the following questions about the force field
F(x,y) = (x²- y², 2xy)
(a) Compute the amount of work done by ♬ in moving a particle in the
counterclockwise direction around the square [0, 1] × [0, 1] along the
path from (0,0) and back to (0,0).
(b) Is F conservative?
(Hint: Can you think of another path from (0,0) to (0,0) whose work
integral is easy to calculate?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1d06251-9cb7-4f37-8e8f-dbbf0e17b22e%2F504c2102-f294-4843-80ea-51922e48faf2%2Flfce3d_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that F is any force field and 7(t) is any constant path. Calculate
SF.d7.
γ
Let y be the boundary of the square [0, 1]×[0, 1] parameterized in the coun-
terclockwise direction, and broken into a concatenation of four straight line
segments V1 * 2 * 3 * 4 as follows:
⚫ Y₁ is the line segment from (0,0) to (1,0)
Y2 is the line segment form (1,0) to (1,1)
3 is the line segment from (1, 1) to (0, 1)
4 is the line segment from (0, 1) to (0,0)
Answer the following questions about the force field
F(x,y) = (x²- y², 2xy)
(a) Compute the amount of work done by ♬ in moving a particle in the
counterclockwise direction around the square [0, 1] × [0, 1] along the
path from (0,0) and back to (0,0).
(b) Is F conservative?
(Hint: Can you think of another path from (0,0) to (0,0) whose work
integral is easy to calculate?)
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