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2. Compute the work done in displacing a particle from the point (-1,2,0) to the point(0,3,1)...
2. Compute the work done in displacing a particle from the point (-1,2,0) to the point(0,3,1) in the force field F(x, y, z) = ,i+j+ k, where r = V x2 + y2 + 22.
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.
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=
2. Find the work done by the force field F(x, y) = 2²7 + ryj on a particle that moves once around the circle r² + y2 = 4 oriented in the counter-clockwise direction.
The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = x, y, z is F(r) = Kr/|r|3 where K is a constant. Find the work done as the particle moves along a straight line from (5, 0, 0) to (5, 3, 5).
(b) Find the work done in moving a particle along the path x-cos y, z 0 from y-0 to y 2m, in the field F(x, y, z)-c" cosy i-xe® sínyi + 2xe2: cos y k. (10 Marks) EvaluatelFdA for surface S: x-z2,0 F(x, y, z)--Зугі + zer cosyj + 3xz2k. (c) y 2,-1 251and (7 Marks)
(b) Find the work done in moving a particle along the path x-cos y, z 0 from y-0 to y 2m, in the field...
(1 point) Find the work done by the force field F(x, y, z) = 5xi + 5yj + 3k on a particle that moves along the helix r(t) = 1 cos(t)i + 1 sin(t)j + 5tk, 0 < t < 21.0
(1, 2) on a particle that moves 2. (5 points) Find the work done by the force field F(x,y) along the line segment from (1,2) to (2,5).
Please solve these three questions!
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...
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).