Question

A force 6i^ + 12j^ + 8k^ produces a displacement of 2i^ + 8j^ + 2k^. Find the work done

Answer 1

$\huge \fcolorbox{red}{pink}{Solution :)}$

Given ,

$\sf \star \: Force = (6 \hat{i} + 12 \hat{j} + 8 \hat{k} ) \: \: n \\ \\\sf \star \: Displacement = (2\hat{i} + 8\hat{j} + 2\hat{k} ) \: \: m$

We know that , the dot product of force and displacement is called work done , so

$\mathbb{ \large \fbox{ \fbox{W = \vec{F} . \vec{S}}}}$

$\sf \leadsto W = (6 \hat{i} + 12 \hat{j} + 8 \hat{k} ).(2\hat{i} + 8\hat{j} + 2\hat{k} ) \\ \\ \sf \leadsto W = (6 \times 2) + (12 \times 8) + (8 \times 2) \\ \\\sf \leadsto W = 12 + 96 + 16 \\ \\\sf \leadsto W = 124 \: \: joule$

Hence , 124 joule is the required answer

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