A particle moves along line segments from the origin to the points (1, 0, 0), (1, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field z2i + 4xyj 4y2k F(x, y, z) Find the work done. F dr
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Q: A particle moves along line segments from the origin to the points (1, 0, 0), (1, 3, 1), (0, 3, 1),…
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A particle moves along line segments from the origin to the points (1, 0, 0), (1, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field
- A particle moves along line segments from the origin to the points (1, 0, 0), (1, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 5xyj + 4y2k. Find the work done.A particle starts at the point (−4, 0), moves along the x-axis to (4, 0), and then along the semicircle y = 16 − x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = 5x, x3 + 3xy2 .A particle starts at the point (-1, 0), moves along the x-axis to (1, 0), and then along the semicircle y = √(1 - x2 )to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = ‹3x, x3 + 3xy2›.
- Line segment D runs from (1, -4, 3) to (2, 0, -1). Determine how much work is done by the force field F(x, y, z) = <3y2/4, sin2(z+3), -cos2(2-y)>Find the work done by the force field 2 2, , , 3 , x y z z z y z z x F in moving a particle along the line segment from (0, 2, 0) to (−4, 3, 2).Find the word done by the force field F (x,y,z)= <x-y2, y-z2, z-x2> on a particle that moves along the line segment from (0,0,1) to (2,1,0)
- A particle moves along line segments from the origin to the points (2, 0, 0), (2, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 3xyj + 4y2k. Use Stokes' Theorem to find the work done. C F · dr =A particle starts at the point (-2,0), moves along the x-axis to (2,0) and then along the semicircle y=radical(4-x^2) to the starting point. Use Green’s Theorem to find the work done on this particle by the force field F(x,y) =(2x,x^3+3xy^2).Find the work done by the vector field ⟨4x+yx,x2+6⟩ on a particle moving along the boundary of the rectangle 0≤x≤3,0≤y≤6 in the counterclockwise direction.(The force is measured in newtons, length in meters, work in joules=(newton-meters).) W=____
- A particle moves along line segments from the origin to the points (1, 0, 0), (1, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 4xyj + 2y2k.A particle starts at the origin, moves along the x-axis to (4, 0), then along the quarter-circle x2 + y2 = 16, x ≥ 0, y ≥ 0 to the point (0, 4), and then down the y-axis back to the origin. Use Green's theorem to find the work done on this particle by the following force field. F(x, y) = sin(x), sin(y) + xy2 + 1 3 x3Suppose you have a vector field F(x,y,z), as defined in the provided image. Find the work that is done by moving a particle in a force field given by F along the following curves: C1, which is a straight line from the origin (0,0,0) to (1,1,1) C2, which is a circle around the origin in the xy-plane with a radius of 3, traversed counterclockwise