Question

Find the work done by the following force field

**F**(*x*, *y*) = 7(*y* +
2)^{5} **i** + 35*x* (*y* +
2)^{4} **j**

in moving an object from *P*(6, −2) to *Q*(5, 0),
along any path

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,z)=6xi+6yj+7k on a
particle that moves along the helix r(t)=5cos(t)i+5sin(t)j+7tk, 0 ≤
t≤ 2π

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.

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

Given the force field F(x, y) = (x − y, 4x + y^2 ), find the
work done to move along a line segment from (0, 0) to (2,0), along
a line segment from (2,0) to (0,1), and then along another line to
the point (−2, 0). Show your work.

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)

Compute the work done by the force F= <sin(x+y), xy,
(x^2)z> in moving an object along the trajectory that
is the line segment from (1, 1, 1) to (2, 2, 2) followed
by the line segment from(2, 2, 2) to (−3, 6, 5) when force is
measured in Newtons and distance in meters.

Find the work done by the force ﬁeld F(x,y,z) = yz i + xz j + xy
k acting along the curve given by r(t) = t3 i + t2 j + tk from the
point (1,1,1) to the point (8,4,2).

Let F~ (x, y, z) = x cos(x 2 + y 2 − z 2 )~i + y cos(x 2 + y 2 −
z 2 )~j − z cos(x 2 + y 2 − z 2 ) ~k be the force acting on a
particle at location (x, y, z). Under this force field, the
particle is moved from the point P = (1, 1, 1) to Q = (0, 0, √ π).
What is the work done by...

if F(x,y)=2xyi+(x^2+2y)j , find the work done by compute fc(F)
*dr , where C is an any path from (0,0) to (-2,1)

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