Question

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.

Answer #1

Find the work done by a force
F = 6i − 8j + 5k
that moves an object from the point
(0, 6, 6)
to the point
(4, 12, 18)
along a straight line. The distance is measured in meters and
the force in newtons.

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>

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).

Compute the line integral with respect to arc length of the
function f(x, y, z) = xy^2 along the parametrized curve 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, 8).

A constant force F=10i+3j−6k moves an object along a straight
line from point (10, 3, 5) to point (8, 9, 9). Find the work done
if the distance is measured in meters and the magnitude of the
force is measured in newtons. Work: nm

2) A varying force F(x,y) = (3x2 – 6xy + 2) i is
applied to an object from (x=2 y=2) to (x=4 y=2). Force is in
Newtons and distances are measured in meters. Find the work
done.

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

Compute the line integral with respect to arc length of the
function
f(x, y, z) = xy2
along the parametrized curve that is the line segment from
(1, 1, 1)
to
(2, 2, 2)
followed by the line segment from
(2, 2, 2)
to
(−6, 6, 1).

Compute the line integral with respect to arc length of the
function f(x, y, z) = xy2 along the parametrized curve
that is the line segment from (1, 1, 1) to (2, 2, 2) followed by
the line segment from (2, 2, 2) to (−9, 6, 3).

An object moving in the xy-plane is subjected to the force F =
2xy i + 3y j N, where x and y are in m.
a. The particle moves from the origin to the point with
coordinates (a, b) by moving first along the x-axis to (a, 0), then
parallel to the y-axis. How much work does the force do?
b. The particle moves from the origin to the point with
coordinates (a, b) by moving first along the...

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