Question

A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field $F(x, y, z) = z^2i + 3xyj + 2y^2k$. Find the work done. $\oint_C F \cdot dr = \text{________}$

Name: a particle moves along line segments from the origin to the points 3 0 0 3 3 1 0 3 1 and back to the origin under the influence of the force field fx y z z2i 3xyj 2y2k find the work done oin 27873
Uploaded: 2023-08-03T04:37:19-08:00
Duration: 5 min 8 s
Channel: Madhur L
Description: a particle moves along line segments from the origin to the points 3 0 0 3 3 1 0 3 1 and back to the origin under the influence of the force field fx y z z2i 3xyj 2y2k find the work done oin 27873

          A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field
$F(x, y, z) = z^2i + 3xyj + 2y^2k$.
Find the work done.
$\oint_C F \cdot dr = \text{________}$

a particle moves along line segments from the origin to the points 3 0 0 3 3 1 0 3 1 and back to the origin under the influence of the force field fx y z z2i 3xyj 2y2k find the work done oin 27873

Added by Carlos W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/03/2023

Step 1

The work done is given by the line integral $\oint_C F \cdot dr$. We can parameterize each segment as follows: $C_1$: $(3t, 0, 0)$, $0 \le t \le 1$ $C_2$: $(3, 3t, t)$, $0 \le t \le 1$ $C_3$: $(3(1-t), 3, 1)$, $0 \le t \le 1$ $C_4$: $(0, 3(1-t), 1-t)$, $0 \le t Show more…

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A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field $F(x, y, z) = z^2i + 3xyj + 2y^2k$. Find the work done. $\oint_C F \cdot dr = \text{________}$