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

Answer:

Step-by-step 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