Question

A force of 26 N along the direction of 5i+12j displaces a body of mass 2kg from point (2,3,4) to (4,3,2). what is the work done by the force?

Answer 1

A force of 26N along the direction of 5i + 12j displaces a body of mass 2kg from the point (2,3,4) to (4,3,2).

first of all, find vector form of force along unit vector of 5i + 12j.
e.g., $\hat{F}=\hat{r}$
here r = 5i + 12j
so, $\frac{\vec{F}}{|F|}=\frac{\vec{r}}{|r|}$

$\vec{F}=26\{\frac{5\hat{i}+12\hat{j}}{\sqrt{5^2+12^2}}\}$

$\vec{F}=10\hat{i}+24\hat{j}$

and displacement vector , $\vec{S}=(4-2)\hat{i}+(3-3)\hat{j}+(2-4)\hat{k}$
$\vec{S}=2\hat{i}+0\hat{j}-2\hat{k}$

now, workdone by force = $\vec{F}.\vec{S}$
= (10i + 24j).(2i - 2k)
= 20 Joule