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Given the force field F =< y,-x>, find the work J² F. dr required to move an object C on the curve consisting of the circle x² + y² = 1 oriented counterclockwise. Hint: parametrize the circle as r(t) first.

Given the force field F =< y,-x>, find the work J² F. dr required to move an object C on the curve consisting of the circle x² + y² = 1 oriented counterclockwise. Hint: parametrize the circle as r(t) first.

Advanced Engineering Mathematics
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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Given the force field \( F = \langle y, -x \rangle \), find the work \( \int_C F \cdot dr \) required to move an object on the curve consisting of the circle \( x^2 + y^2 = 1 \) oriented counterclockwise. Hint: parametrize the circle as \( \mathbf{r}(t) \) first.
Transcribed Image Text:Given the force field \( F = \langle y, -x \rangle \), find the work \( \int_C F \cdot dr \) required to move an object on the curve consisting of the circle \( x^2 + y^2 = 1 \) oriented counterclockwise. Hint: parametrize the circle as \( \mathbf{r}(t) \) first.
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