Question

6. A force 7 = (4ỉ + 5j) N displaces a body by (sî - 4ſ)
m. Find the work done by the force.
Ans. zero

Answer 1

Answer:

$\boxed{\mathfrak{Work \ done \ by \ the \ force = zero}}$

Given:

Force $\rm (\overrightarrow{F}) = 4 \hat{i} + 5\hat{j}$

Displacement $\rm (\overrightarrow{d}) = 5 \hat{i} - 4 \hat{j}$

Explanation:

Work done (W) is dot product of force vector and displacement vector i.e.

$\boxed{ \bold{ W = \overrightarrow{F}.\overrightarrow{d}}}$

By substituting values in the equation we get:

$\rm \implies W = (4\hat{i} + 5\hat{j} ).(5\hat{i} - 4\hat{j} ) \\ \\ \rm \implies W =4 \times 5 - 5 \times 4 \\ \\ \rm \implies W = 20 - 20 \\ \\ \rm \implies W = 0 \: J$

Answer 2

Given ,

Force (f) = { 4i + 5j } N

Displacement (s) = { 5i - 4j } m

We know that , the work done is defined as the dot or scalar product of force and displacement

Mathematically ,

$\boxed{ \tt{Work \: done \: (w) = \vec{f}.\vec{s}}}$

Thus ,

w = { 4i + 5j } . { 5i - 4j }

w = {4 × 5} + { 5 × (-4) }

w = 20 - 20

w = 0 J

Therefore , the work done is 0 J

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