Find the work done by the vector field F(x, y) = {xy i + áraj (the...
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=
9. The work done by the force F(x, y) (2at +e) i (4y in moving a particle -re from (0,0) to (1,1) along the curve y =x4 needs to be calculated. a. Show that F is a conservative vector field. b. Describe three different ways to calculate the work. Answer: 3 +1/e c. Calculate the work by a method of your choice.. a. Show that F=(y+yz) i + (x + 32 + xz) j +(9yz2 + y 1) k is...
Q6 [10+1+3=14 Marks] Let F be a force field given by F(x, y) = y2 sin(xy?) i + 2xy sin(xy?)j. (a) Show that F. dr is exact by finding a potential function f. (b) Is I = S, y2 sin(xy2) dx + 2xy sin(xy?) dy independent of path C? Justify your answer. (c) Use I to find the work done by the force field F that moves a body along any curve from (0,0) to (5,1).
Find the work done by the force field F(x, y, z) = (x – y, x + z, y + z) in moving a particle along the line segment from (0,0,1) to (2, 1, 0).
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,...
Evaluate ScF. dr where F(x, y) = xy?i + xyºj and C is the polygonal path from (0,0) to (1,0) to (0,1) to (0,0) Select one: O a. 30 1 O b. 35 c. 110 O d. - 3
A force acting on a particle moving in the xy-plane is given by F = (2x3y4i+x2y3j), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x=5.00 m and y = 5.00 m as shown in the figure. Calculate the work W = F(r) dr done by F on the particle as it moves along a) The purple path b) The red path
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
Find the work done by the force field F on a particle moving along the given path. F(x, y) = xi + 4yj C: x = t, y = 13 from (0, 0) to (2,8)