Question

On applying a force F

= (3i − 4j + 9k )N on an object

the body get displaced S = (3i + 4j + 8k) m. Calculate the

work done by force?​

Answer 1

Answer:

65 Joule

Explanation:

W=F.S

(3i-4j+9k).(3i+4j+8k)

9-16+72

= 65 joule

Answer 2

Given :

• $\mathtt{F = (3\hat{i} - 4\hat{j} +9\hat{k})N}$

• $\mathtt{S = (3\hat{i} + 4\hat{j} +8\hat{k})m }$

To find :

• Work done by the force

Solution :

The work done by an object is a scalar product of force and displacement .

Hence ,

$\leadsto \mathtt{W = \overrightarrow{F}.\overrightarrow{s}}$

Now let's substitute the given values in the above equation ,

$\leadsto \mathtt{W = (3\hat{i} - 4\hat{j} +9\hat{k}).}(3\hat{i} + 4\hat{j} +8\hat{k})$

Note :

$\leadsto \mathtt{\overrightarrow{A}.\overrightarrow{B}}= {(a\hat{i} + b\hat{j} +c\hat{k}).(e\hat{i} + f\hat{j} +g\hat{k})}\\ \\ \leadsto \mathtt{\overrightarrow{A}.\overrightarrow{B} = a . e + b.f +c.g }$

Hence ,

$\leadsto \mathtt{W = 3 \times 3 + (-4 \times 4 ) + 9 \times 8 }$

$\leadsto \mathtt{W = 9 - 16 + 72 }$

$\leadsto \mathtt{W = 81 - 16 }$

$\leadsto\underline{\boxed{\mathtt{W = 65 J }}}$

The work done by the force is 65 J