Question

Find work done by a force $\overrightarrow{F}=x\hat{i}+xy\hat{j}$ acting on a particle to displace it from point O(0, 0) to C(2, 2).

Answer 1

$W={\int }_a^b$ $\overrightarrow{F}$ . $\overrightarrow{dr}$

$\overrightarrow{dr}$=$dx\hat{i}$+$dy\hat{j}$+dz$\hat{k}$

$W$=${\int }_0^2$xdx + ${\int }_0^2$xydy

On substituting the limits we get,

$W=(2+4x)J$