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d) A vector field is given by F(x,y,2) = 2xj+ (x² - y(1-y))k . 2(1-e"?) Find the work that the vector field performs by moving from start to finish point along curve C. e) Calculate the total work that the vector field does by walking along C from start to end point then move along a straight line back to the starting point. Can you determine if the vector field is conservative just by calculating this working integral? Justify the answer.

d) A vector field is given by F(x,y,2) = 2xj+ (x² - y(1-y))k . 2(1-e"?) Find the work that the vector field performs by moving from start to finish point along curve C. e) Calculate the total work that the vector field does by walking along C from start to end point then move along a straight line back to the starting point. Can you determine if the vector field is conservative just by calculating this working integral? Justify the answer.

Advanced Engineering Mathematics
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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Vector calculus 

 

Please solve part (d) and (e)

A parametric curve C is given by the position vector r(t) sin (2t), sin (t),e' Osis". 2 a) Find the tangent vector at the point P given by t = 4 b) Determine the tangent component of the acceleration vector and the normal component in P. c) c) A thread has the shape given by the curve C, and mass per. length given by the function 2z? 8(z) =- (1+z*)* * Calculate the mass of the thread. d) A vector field is given by F(x,y,z) = 2xj+ 2(1-eri (** -y(1-y)Ā. Find the work that the vector field performs by moving from start to finish point along curve C. e) Calculate the total work that the vector field does by walking along C from start to end point then move along a straight line back to the starting point. Can you determine if the vector field is conservative just by calculating this working integral? Justify the answer.
Transcribed Image Text:A parametric curve C is given by the position vector r(t) sin (2t), sin (t),e' Osis". 2 a) Find the tangent vector at the point P given by t = 4 b) Determine the tangent component of the acceleration vector and the normal component in P. c) c) A thread has the shape given by the curve C, and mass per. length given by the function 2z? 8(z) =- (1+z*)* * Calculate the mass of the thread. d) A vector field is given by F(x,y,z) = 2xj+ 2(1-eri (** -y(1-y)Ā. Find the work that the vector field performs by moving from start to finish point along curve C. e) Calculate the total work that the vector field does by walking along C from start to end point then move along a straight line back to the starting point. Can you determine if the vector field is conservative just by calculating this working integral? Justify the answer.
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