Mathematics: Find the work done by the force field f(x, y, z) = x − y 2, y − z2, z − x2 on a particle that moves along the line segment from (0, 0, 1) to (3, 1, 0).

Find the work done by the force field f(x, y, z) =

Ответ:

JellalFernandes

14.03.2022

Parameterize the line segment by

$\mathbf r(t)=\langle0,0,1\rangle(1-t)+\langle3,1,0\rangle t$
$\mathbf r(t)=\langle3t,t,1-t\rangle$

with $0\le t\le1$ . Then the work done along the path (call it $\mathcal C$ ) is

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\mathbf f(\mathbf r(t))\cdot\mathrm d\langle3t,t,1-t\rangle$
$=\displaystyle\int_0^1\langle3t-t^2,t-(1-t)^2,1-t-(3t)^2\rangle\cdot\langle3,1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(5t^2+13t-2)\,\mathrm dt=\frac{37}6$

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Ответ:

pinkpearl20

17.12.2020

Mathematics

Step-by-step explanation: I think it’s C because if you change Y you have to change X so when you flip it, the y decreases by 2 and stays in the same X spot.

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Find the work done by the force field f(x, y, z) = x − y 2, y − z2, z − x2 on a particle that moves along the line segment from (0, 0, 1) to (3, 1, 0).

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