First slide

Work

Question

A particle moves from position ${\vec{r}}_{1} = 3 \hat{i} + 2 \hat{j} - 6 \hat{k}$ to position ${\vec{r}}_{2} = 14 \hat{i} + 13 \hat{j} + 9 \hat{k}$ under the action of force $4 \hat{i} + \hat{j} + 3 \hat{k} N .$ The work done will be

Easy

A

100 J
B

50 J
C

200 J
D

75 J

Solution

$W = \vec{F} . (\vec{r_{2}} - \vec{r_{1}}) = (4 \hat{i} + \hat{j} + 3 \hat{k}) (11 \hat{i} + 11 \hat{j} + 15 \hat{k})$
$W = 44 + 11 + 45 = 100 Joule$

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