Question

A constant unit force vector makes angle 30 with the positive x - axis. Find the work done by the force in moving the object 13 units in the direction of the positive x - axis. g

Answer 1

Explanation:

Force, F = 1 unit makes 30° from X axis

displacement, S = 13 units along + X axis

Write the force and the displacement in vector form

`\overrightarrow{F}=1\left ( Cos30\widehat{i}+Sin30\widehat{j} \right )`

`\overrightarrow{F}=0.866\widehat{i}+0.5\widehat{j}`

`\overrightarrow{S}=13\widehat{i}`

Work is defined as the dot product of force and the displacement vector.

`W=\overrightarrow{F}.\overrightarrow{S}`

`W=\left (0.866\widehat{i}+0.5\widehat{j} \right ) . 13\widehat{i}`

W = 11.26 units