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Longitudinal Strain

A force given...

Question

A force given by $\to F = f_{x}^i + f_{y}^j + f_{z}^k$ , acts on a particle which moves from (a,b,c) to (d,e,f) . The work done by the force $F$ is (Here $A_{1}, A_{2}, A_{3}$ are magnitudes of area bounded)

A_{1} + A_{2} + A_{3}

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A_{1} - A_{2} - A_{3}

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- A_{1} + A_{2} - A_{3}

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A_{1} - A_{2} + A_{3}

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Solution

The correct option is A $A_{1} - A_{2} - A_{3}$
$w = \int_{a}^{d} f_{x} d x + \int_{b}^{e} f_{y} d y + \int_{c}^{f} f_{z} d z$
Along x direction:
Now $\int_{a}^{d} f_{x} d x$ is positive since $f_{x} > 0$ and $d > a$
Along y direction:
$\int_{b}^{e} f_{y} d y$ is negative since $f_{y} > 0; e < b$
Along z direction:
$\int_{c}^{f} f_{z} d z$ is negative $f_{z} < 0; f > c$
$∴ w = + A_{1} - A_{2} - A_{3}$

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