Question

A practice is acted by constant force 3i-j+2k,-i+3j+k and i+j-2k and is displaced from the point (-1,2,3)to(2,-1,5).calculate the total work done by the force

Answer 1

$\large\underline{\underline{\sf Given:}}$

• $\sf{F_1=3\hat{i}+\hat{j}-2\hat{k}}$

• $\sf{F_2=-\hat{i}+3\hat{j}+\hat{k}}$

• $\sf{F_3=\hat{i}+\hat{j}-2\hat{k}}$

• Distance $\sf{(r_1)=-\hat{i}+2\hat{j}+3\hat{k}}$

• Distance $\sf{(r_2)=2\hat{i}+-\hat{j}+5\hat{k}}$

$\large\underline{\underline{\sf To\:Find:}}$

• Total work done by force (W) =?

$\large\underline{\underline{\sf Solution:}}$

$\sf{F_1+F_2+F_3(F)=(3\hat{i}-\hat{j}+2\hat{k})+(-\hat{i}+3\hat{k})+(\hat{i}+\hat{j}-2\hat{k})}$

$\large{\sf F=(3\hat{i}+3\hat{j}+\hat{k}) }$

$\large\implies{\sf \triangle r=r_2-r_1 }$

$\large\implies{\sf \triangle r=(2\hat{i}-\hat{j}+5\hat{k})-(-\hat{i}+2\hat{j}+5\hat{k})}$

$\large\implies{\sf \triangle r=(3\hat{i}-3\hat{j}+2\hat{k})}$

$\large{\boxed{\sf Work=F\triangle r }}$

$\implies{\sf W=(3\hat{i}+3\hat{j}+\hat{k}).(3\hat{i}-3\hat{j}+2\hat{k})}$

$\large\implies{\sf W= 9-9+2}$

$\large\implies{\sf W=0+2}$

$\large\implies{\sf W=2J }$

$\large\underline{\underline{\sf Answer:}}$

•°• Total work done by force is 2J