Question

An ant slides from point (0, 0) to (3, 4, 6) under the wind force $\overrightarrow{F}=(2x\hat{i}+4\hat{j}+6z\hat{k})$. Find the work

done by the force of wind in Joules.

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Answer 1

$w=\underset{\overrightarrow{r_1}}{\overset{\overrightarrow{r_2}}{\int }}\overrightarrow{F}.\overrightarrow{dr}$

= $\underset{(0,0)}{\overset{(3,4,6)}{\int }}(2x\hat{i}+4\hat{j}+6z\hat{k}).(dx\hat{i}+dy\hat{j}+dz\hat{k})$

= $\underset{x_1}{\overset{x_2}{\int }}2xdx+\underset{y_1}{\overset{y_2}{\int }}4dy+\underset{21}{\overset{22}{\int }}6zdz$

= $\frac{2x^2}{2}{|}_0^3+4y{|}_0^4+\frac{{62}^2}{2}{|}_0^6$

= $89+16+108$

$W=133Joules$