QUESTION 10 (a) Verify that the force field F = yi+zj+4k s conservative. By finding its potential function ф, evaluate...
4. Use Green's Theorem to calculate the work done by force F on a particle that is moving counterclockwise around the closed path C. Determine whether the vector field is conservative. C boundary of the triangle with vertices (0,0), (V5,0), (0,15). F(x,y) = (x3 - 3y)i + (6x +5/7);.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1) to B(0,3) depicted in Figure 1 Figure 1. Rectangular path of the particle. Compute the work done by the force in this field; Using line integral (if the integral is difficult to evaluate, then use Matlab) b. Also using Green's Theorem without computer aid. Compare your results. a.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the...
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,...
Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path F(x,y) = (ex – 4y)i + (ey + 7x)j C: r = 2 cos(0) -11 POINTS LARCALC11 15.4.028.MI. MY NOTES ASK YOUR TEACHER Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path F(x, y) = (5x2 + y)i + 3xy?j C: boundary of...
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S = F (potential function). (5) Use the results in part(a) to cakulae ( F. ds along C which the curve y = a* from (0,0) to (2,16). (2) Use Green's Theorem to evaluate 1. F. ds. F(1,y) =(yº+sin(26))i + (2xy2 + cos y)and C is the unit circle oriented counter clockwise (6) Evaluate the surface integral || 9. ds. F(x,y,z) = xi +++where S...
Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C. F(x, y) = (3x2+y)i + 3xy2jC: boundary of the region lying between the graphs of y = √x. y = 0, and x = 1
there is first question E then there is the question
of the value of the line integral ,then quwstion A, then question
1, and the last two pictures are one question
Question E (5 points) By Green's theorem, the value of the line integral y 4 is: , where C is the curve given by a) 3 c) 12t d) 27T e) If none of the above is correct, write your answer here in a box rover the line segment...
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 +...