Question

If the two forces f1= 2i +4j +4k and F2 = 2i +5j
acts on one body and displacment it forms(1,0,0) to (2,1,1) find the net work done.​

Answer 1

Answer is in the pic.

Answer 2

Given:

The two forces f1= 2i +4j +4k and F2 = 2i +5j

acts on one body and displacment it forms(1,0,0) to (2,1,1) .

To find:

New work done.

Calculation:

Net force F_(net) :

$\therefore \: \vec{F}_{net} =( 2 \hat{i} + 4 \hat{j} + 4 \hat{k}) + (2 \hat{i} + 5 \hat{j})$

$= > \vec{F}_{net} = 4 \hat{i} + 9\hat{j} + 4 \hat{k}$

Now , net displacement vector:

$\therefore \: \vec{d} = (2 \hat{i} + \hat{j} + \hat{k}) - ( \hat{i})$

$= > \: \vec{d} = \hat{i} + \hat{j} + \hat{k}$

Now , net work done :

$\therefore \: work = \vec{F}_{net} \: . \: \vec{d}$

$= > \: work = (4 \hat{i} + 9 \hat{j} + 4 \hat{k}) \: . \: ( \hat{i} + \hat{j} + \hat{k})$

$= > \: work = (4 \times 1) + (9 \times 1) + (4 \times 1)$

$= > \: work = 4 + 9 + 4$

$= > \: work = 17 \: joule$

So, final answer is:

$\boxed{ \bf{\: work = 17 \: joule}}$