Use Green’s Theorem to find the work done by the force field F on a particle that moves along the stated path. F x , y = x y i + 1 2 x 2 + x y j ; the particle starts at 5 , 0 , traverses the upper semicircle x 2 + y 2 = 25 , and returns to its starting point along x -axis .
Use Green’s Theorem to find the work done by the force field F on a particle that moves along the stated path. F x , y = x y i + 1 2 x 2 + x y j ; the particle starts at 5 , 0 , traverses the upper semicircle x 2 + y 2 = 25 , and returns to its starting point along x -axis .
Use Green’s Theorem to find the work done by the force field F on a particle that moves along the stated path.
F
x
,
y
=
x
y
i
+
1
2
x
2
+
x
y
j
;
the particle starts at
5
,
0
,
traverses the upper semicircle
x
2
+
y
2
=
25
,
and returns to its starting point along
x
-axis
.
Find the outward flux of F = (4x + 25y²,0.
10z
through the surface
3
= 1.
25
4
+y
-n CI
Č2
FIGURE Q3(b)
A force field is given by the equation. A particle is moved from (1,0,0) to (1,1,1) along a straight line. Calculate the work done by the force field on the particle.
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