Looking for classes? Ksquare Career Institute, Bengaluru →
Work done by a constant force (dot product)
-
A particle moves from a point $(-2\hat{i} + 5\hat{j})$ to $(4\hat{j} + 3\hat{k})$ when a force of $(4\hat{i} + 3\hat{j})$ N is applied. How much work has been done by the force?
$W = \vec{F}\cdot\Delta\vec{r}$.
Displacement $\vec{s} = (4\hat{j} + 3\hat{k}) - (-2\hat{i} + 5\hat{j}) = 2\hat{i} - \hat{j} + 3\hat{k}$
$W = \vec{F}\cdot\vec{s} = (4\hat{i} + 3\hat{j})\cdot(2\hat{i} - \hat{j} + 3\hat{k}) = 8 - 3 = 5$ J