If the integral SF - dl is regarded as the work done in moving a particle from A to B, find the work done by the force field F = 2xyax + (x²z²)a, - 3xz²a₂ on a particle that travels from A(0, 0, 0) to B(2, 1, 3) along → (a) The segment (0, 0, 0) → (0, 1, 0) → (2, 1, 0) (2, 1, 3) (b) The straight line (0, 0, 0) to (2, 1, 3)
If the integral SF - dl is regarded as the work done in moving a particle from A to B, find the work done by the force field F = 2xyax + (x²z²)a, - 3xz²a₂ on a particle that travels from A(0, 0, 0) to B(2, 1, 3) along → (a) The segment (0, 0, 0) → (0, 1, 0) → (2, 1, 0) (2, 1, 3) (b) The straight line (0, 0, 0) to (2, 1, 3)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![If the integral \( \int_A^B \mathbf{F} \cdot d\mathbf{l} \) is regarded as the work done in moving a particle from \( A \) to \( B \), find the work done by the force field
\[
\mathbf{F} = 2xy\mathbf{a}_x + (x^2 - z^2)\mathbf{a}_y - 3xz^2\mathbf{a}_z
\]
on a particle that travels from \( A(0, 0, 0) \) to \( B(2, 1, 3) \) along
(a) The segment \( (0, 0, 0) \rightarrow (0, 1, 0) \rightarrow (2, 1, 0) \rightarrow (2, 1, 3) \)
(b) The straight line \( (0, 0, 0) \) to \( (2, 1, 3) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bf62d6d-db44-481f-809c-2b5fe2fdf00c%2F7e25bc03-c7f9-4b97-90a3-f1fbd12babdd%2Fht8686a_processed.png&w=3840&q=75)
Transcribed Image Text:If the integral \( \int_A^B \mathbf{F} \cdot d\mathbf{l} \) is regarded as the work done in moving a particle from \( A \) to \( B \), find the work done by the force field
\[
\mathbf{F} = 2xy\mathbf{a}_x + (x^2 - z^2)\mathbf{a}_y - 3xz^2\mathbf{a}_z
\]
on a particle that travels from \( A(0, 0, 0) \) to \( B(2, 1, 3) \) along
(a) The segment \( (0, 0, 0) \rightarrow (0, 1, 0) \rightarrow (2, 1, 0) \rightarrow (2, 1, 3) \)
(b) The straight line \( (0, 0, 0) \) to \( (2, 1, 3) \)
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