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2. A) Calculate the work done by the field } = (x² - y2,-2xy) when moving...
Find the work done by the force field F= (y2/2, Z, x) in moving a particle along the curve C, where C is the intersection curve of the plane x +z = 1 and the ellipsoid x2 + 2y2 + x2 = 1 oriented counterclockwise when viewed from positive z— axis.
(6) Fundamental Theorem of Line Integrals F = <M,N> = < 2xy, x² + y2 > (6a) Show that F is a Conservative Vector Field. (6b) Find the Potential Function f(x,y) for the Vector Field F. (60) Evaluate W = | Mdx + Ndy from (5,0) to (0,4) over the path C: È + K3 = 1 с
Calculate the work done by the force F= (x-2y)i+(x+y)j in a) 2. moving from point A at (0,2) to point B at (2,18) along the path y 4x2+2. [5 marks] - Evaluate the line integral(xdy+ydx) along a path C that is b) [5 marks] to t described by x= cos(f), y=2sin(t)+5, from t =: 2 Calculate the work done by the force F= (x-2y)i+(x+y)j in a) 2. moving from point A at (0,2) to point B at (2,18) along the...
Given the potential V = 2xy?, calculate the work done by the field moving a 10 uC charge from point A (1,3,4) to point B (2,5,8). Assume the potential is given in volts.
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,...
Find the work done by the inverse-square force field in moving a particle from (1,0,0) to (0,3,4). Integrate first along the line segment from (1,0,0) to (5,0,0) and then along a path on the sphere with equation x2+y2+z2= 25. Why is the second integral automatically zero? 2213/2 2213/2
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 +...
HELP Calculate the work done by the force field F on an object moving along a curve from P(-5, 1) to Q(7,2). F(x, y) =
A particle in the xy plane travels along a spiral path C beginning at a point P that is 8 units from the origin and ending at a point Q that is 2 units from origin. The particle makes 2.5 revolutions aroung the origin along the way. What is work done by the gravitational field F(x, y) = i + j in moving the particle along its path? (x2 + y2) 3/2)