A small particle moves to position 5 i ^ - 2 j ^ + k ^ from its initial position 2 i ^ + 3 j ^ - 4 k ^ under the action of force 5 i ^ + 2 j ^ + 7 k ^ N . The value of work done will be ______ J .

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TestHub · Accepted Answer

Work done by a constant force is given by $W = Force (\vec{F}) \cdot Displacement (\vec{r})$ , where, $\vec{r} = {\vec{r}}_{2} - {\vec{r}}_{1}$

Given here, $\vec{r_{1}} = 5 \hat{i} - 2 \hat{j} + \hat{k}$ and ${\vec{r}}_{2} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$

So, $W = \vec{F} \cdot ({\vec{r}}_{2} - {\vec{r}}_{1})$

$= (5 \hat{i} + 2 \hat{j} + 7 \hat{k}) \cdot [(5 \hat{i} - 2 \hat{j} + \hat{k}) - (2 \hat{i} + 3 \hat{j} - 4 \hat{k})]$

$\Rightarrow W = 40 J$

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