Question

Three constant force $\overline{F_1}=2\hat{i}-3\hat{j}+2\hat{k},\overline{F_2}=\hat{i}+\hat{j}-\hat{k}$ and $\overline{F_3}=\hat{j}-2\hat{k}$ in newton act on a particle The particle can only move,from $(1,-1,2)$ to $(-1,-1,3)$ and then to $(2,2,0)$ (displacement being measured in metre ). Find the total work done by the forces

Answer 1

$\overrightarrow{F_{net}}=\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}$

$=(2+1+0)\hat{i}+(-3+1+1)\hat{j}+(2,-1,-2)\hat{k}$

$=3\hat{i}-\hat{j}-\hat{k}$

$\overrightarrow{S_1}=-2\hat{i}+0\hat{j}+\hat{k}$

$\overrightarrow{S_2}=3\hat{i}+3\hat{j}-3\hat{k}$

Work 1= $\overrightarrow{F_{net}}.\overrightarrow{S_1}=-6-1=-7J$

Work 2=$\overrightarrow{F_{net}}.\overrightarrow{S_2}=9-3+3=9J$

work net =$-7+9$.

$=2J$