Question

object replaced from 3(i)^ +2(j)^ to 14(j)^ +13(i)^ by a force 4(i)^ + (j)^ . Calculate work done by force

Answer 1

$\huge\underline\blue{\sf Answer:}$

$\red{\boxed{\sf Work\:done\:by\:force≈140J }}$

$\huge\underline\blue{\sf Solution:}$

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

• $\sf{r_1=3\hat{i}+2\hat{j}}$

• $\sf{r_2=14\hat{j}+13\hat{i}}$

• $\sf{Force(F)=4\hat{i}+\hat{j}}$

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

• Work done (W) = ?

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large{\boxed{\sf r=r_2-r_1}}$

$\large\implies{\sf r=13\hat{i}+14\hat{j}-3\hat{i}+2\hat{j} }$

$\large\implies{\sf r=10\hat{i}+12\hat{j}}$

Work (W) = Force ×Distance

$\large\implies{\sf (4\hat{i}+\hat{j})-(10\hat{i}+12\hat{j})}$

$\large\implies{\sf 140\hat{i}+12\hat{j}}$

$\large\implies{\sf \sqrt{(140)^2+(12)^2}}$

$\large\implies{\sf \sqrt{19744}}$

$\large\implies{\sf ≈140J}$

$\red{\boxed{\sf Work\:done\:by\:force≈140J }}$