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) = hitj+, k, where r = Vx2 + 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=
(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
(10 points) The work done by a force is the scalar product of the force and displacement vectors, i.e W F x and the power is given by the dot product between the force and the velocity vector, i.e. P F.V . For a force vector, F 2x i+10y j- (x+5y) k and a displacement vector, x=t i+t j+2t k, calculate the work done by the force and the power required. Based on your answer, what can you say about...
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)
Q2: Use Green's Theorem to find the work done by the force field F (e* -y3) i+ (cosy+ x3)j particle that travels once around the circle x2 + y2 = 1 in the counterclockwise direction. on a Q3:
Q2: Use Green's Theorem to find the work done by the force field F (e* -y3) i+ (cosy+ x3)j particle that travels once around the circle x2 + y2 = 1 in the counterclockwise direction. on a Q3:
(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...
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
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...