Question

A force F = (5 i + 4 j) N acts on an object as it moves in the x direction from the origin to x= 2 m. Here the i and j denote the

unit vectors in the x and y direction. The work done by the object is​

Answer 1

Answer:

$\boxed{\mathfrak{Work \ done \ by \ the \ object = 10 \ J}}$

Given:

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

Displacement $\rm (\overrightarrow{d}) = 2 \hat{i} + 0 \hat{j}$

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:

$\rm \implies W = (5\hat{i} + 4\hat{j} ).(2\hat{i} + 0\hat{j} ) \\ \\ \rm \implies W =5 \times 2 + 4 \times 0 \\ \\ \rm \implies W = 10 + 0\\ \\ \rm \implies W = 10 \: J$

Answer 2

Answer:

W = (5i + 4j).(2i)

W = 10 J