Q6 [10+1+3=14 Marks] Let F be a force field given by F(x, y) = y2 sin(xy?)...
Find the work done by the vector field F(x, y) = {xy i + áraj (the vector field from Question 1) on a particle that moves from (0,0) to (0, 1) (moving in a straight line up and along the y axis) and then from (0, 1) to (3, 2) along the curvey= Vx+1. Thus the path is given by along the curve y=x+1 (0,0) up the y-axis + (0,1) (3,2) 1 F. dr 2 F. dr = 0 18...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
Find the work done by the force field F on a particle that moves along the curve C. F(x,y)=xy i+x^2 j C: x=y2 from (0,0) to (4,2) Enter the exact answer as an improper fraction, if necessary. W=
Chapter 15, Section 15.2, Question 045 Find the work done by the force field F on a particle that moves along the curve C. F(x,y) = 2xy i + 2x j C: x= y2 from (0,0) to (8,2) Enter the exact answer as an improper fraction, if necessary. W= ? Edit
In each of the following exercises, you are given a force field F = F(x, y), in Newtons, and a oriented, closed curve C in the xy-plane, where x and y are in meters. Use Green's Theorem to calculate the work done by F along C. 9. F(x, y) = (2,5 – yº, x3 – y5), and C is the curve which starts at (0,0), moves along a line segment to (1/V2,1/V2), moves counterclockwise along the circle of radius 1,...
Find the work done by the force field F on a particle that moves along the curve rve C. F(x,y) = 2xy i+ 3x j C: x=y from (0,0) to (1,1) Enter the exact answer as an improper fraction, if necessary. 1 W= Edit 2
Problem 5 (10 points) Calculate the work done by a force field F, given by F(x, y) = (x + y, x - y) when an object moves from (0,0) to (1,1) along the path x = y2.
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
F(x, y,z)=(y2 +e", 2xy + z sin y, cos y) is a gradient vector field. Compute Sc F. dr where C=GUC,, C işthe curve y = x^, z = 0 from (0,0,0) to (1,1,0) and C, is the straight line from (1,1,0) to (2,2,3)
2. The force F(x, y) = (y + 2x) sin(xy + x)i + x sin(xy + x2) is conservative. (a) Find a potential V such that F = -VV. [2 marks] (b) Is F central? Provide a reason for your answer. [2 marks]