Question

a particle is pushed by a force 2i+3j-2k & 5i-j-3k simultaneously and displaced from point i+j+k to point 2i-j+3k what is the work done?​

Answer 1

Given:

• Forces pushing the particle are : 2i+3j-2k & 5i-j-3k
• Displacement is from i+j+k to 2i-j+3k.

To find:

• Work done by force ?

Calculation:

First of all, let's find net force :

$\vec{F}= (2 \hat{i} + 3 \hat{j} - 2 \hat{k}) + (5 \hat{i} - \hat{j} - 3 \hat{k})$

$\implies \vec{F} = 7 \hat{i} + 2 \hat{j} - 5\hat{k}$

Now, let's find net displacement:

$\vec{d} = (2 \hat{i} - \hat{j} + 3 \hat{k}) - ( \hat{i} + \hat{j} + \hat{k})$

$\implies \vec{d} = \hat{i} - 2\hat{j} + 2\hat{k}$

Now, work will be dot product between force vector and displacement vector :

$W = \vec{F}. \vec{d}$

$\implies \: W = (7 \hat{i} + 2 \hat{j} - 5 \hat{k}).( \hat{i} - 2 \hat{j} + 2 \hat{k})$

$\implies \: W = 7- 4 - 10$

$\implies \: W = -7 \: joule$

So, work done by force is -7 Joule.