Question

121 - A particle moves from position r1 = (3i +2j-6k) to
postion r2 = (14i + 13j + 9k) N.Under the action of force
(4i + j + 3k). Calculate the work done

Answer 1

Answer:

$\boxed{\mathfrak{Work \ done = 100 \ J}}$

Given:

$\rm \vec{r_1} = 3 \hat{i} + 2\hat{j} - 6 \hat{k}$

$\rm \vec{r_2} = 14 \hat{i} + 13\hat{j} + 9 \hat{k}$

$\rm \overrightarrow{F} = 4 \hat{i} + \hat{j} + 3 \hat{k}$

Explanation:

Work done (W) is dot product of force vector and displacement vector i.e.

$\boxed{ \bold{ W = \overrightarrow{F}.\overrightarrow{d}}}$

So,

$\rm \implies W = \overrightarrow{F}.(\overrightarrow{r_2} - \overrightarrow{r_1}) \\ \\ \rm \implies W = (4\hat{i} + \hat{j} + 3 \hat{k}).(14\hat{i} + 13\hat{j} + 9 \hat{k} - (3\hat{i} + 2\hat{j} - 6 \hat{k}) \\ \\ \rm \implies W = (4\hat{i} + \hat{j} + 3 \hat{k}).(14\hat{i} + 13\hat{j} + 9 \hat{k} - 3\hat{i} - 2\hat{j} + 6 \hat{k}) \\ \\ \rm \implies W = (4\hat{i} + \hat{j} + 3 \hat{k}).(11\hat{i} + 11\hat{j} + 15 \hat{k}) \\ \\ \rm \implies W =4 \times 11 + 1 \times 11 + 3 \times 15 \\ \\ \rm \implies W =44 + 11 + 45 \\ \\ \rm \implies W =100 \: J$