Question

Using Stoke's Thm, find the work done by the vector field F(x, y, z) = 〈z, x, y〉, that moves an object along the triangle with vertices P(1, 0, 0), Q(0, 1, 0), R(0, 0, 1), in a counterclockwise manner, starting and ending at P.

Answer #1

Find the work done by a force field F (x, y) = 3x^2i + (4x +
y^2)j on a particle that moves along the curve x^2+y^2 =1 for which
x>=0 and y>=0 (counterclockwise)

find the work done by the force field f(x,y)= <
x2+y2, -x > on a particle that moves along
the curve c: x2+y2=1, counterclockwise from
(0,1) to (-1,0)

Find the work done by the force field
F(x,y,z)=2xi+2yj+7kF(x,y,z)=2xi+2yj+7k
on a particle that moves along the helix
r(t)=3cos(t)i+3sin(t)j+4tk,0≤t≤2π

Find the work done by the force field F(x,y,z)=6xi+6yj+7k on a
particle that moves along the helix r(t)=5cos(t)i+5sin(t)j+7tk, 0 ≤
t≤ 2π

Find the work done by the vector field F = 〈 2 xy + z/y , x^2 −
xz/ y^2 , x/y 〉 and C is the line segment that goes from (1,3,2) to
(1,4,6).

Find the work done by the following force field
F(x, y) = 7(y +
2)5 i + 35x (y +
2)4 j
in moving an object from P(6, −2) to Q(5, 0),
along any path

For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a
function f(x, y) such that F~ (x, y) = ∇f(x, y) = h ∂f ∂x , ∂f ∂y i
by integrating P and Q with respect to the appropriate variables
and combining answers. Then use that potential function to directly
calculate the given line integral (via the Fundamental Theorem of
Line Integrals):
a) F~ 1(x, y) = hx 2 , y2 i Z C F~ 1...

find the work done in the force camp F(x,y,z)=<xz,xy,zy> in a
particle that moves along the curve <t^2,-t^3,t^4> for 0
<= t <= 1
THE
F is F(x,y,z)= <xz,yx,zy>

Consider the vector field below: F ⃗=〈2xy+y^2,x^2+2xy〉 Let C be
the circular arc of radius 1 starting at (1,0), oriented counter
clock wise, and ending at another point on the circle. Determine
the ending point so that the work done by F ⃗ in moving an object
along C is 1/2.

. Find the flux of the vector field F~ (x, y, z) =
<y,-x,z> over a surface with downward orientation, whose
parametric equation is given by r(s, t) = <2s, 2t, 5 − s 2 − t 2
> with s^2 + t^2 ≤ 1

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