Question

A body constrained to move along Z-axis of a coordinate system is subjected to a constant force $F$ given by $F =-\hat{i ⁡}+2\hat{j ⁡}+3\hat{k}N⁡$ where $\hat{i}$ , $\hat{j}$ and $\hat{k}$ are the unit vector along the X, Y and Z-axis of the system respectively. What is the work done by this force in moving the body a distance of $4 \, m$ along the Z-axis?

• A. $12J$
• B. $13J$
• C. $10J$
• D. $9J$

Answer 1

Answer: (A)

Force, $F =\left(- \hat{\text{i}} + 2 \hat{\text{j}} + 3 \hat{k}\right)\text{N}$
Displacement, $s =\left(4 \hat{k}\right)\text{m}=\left(0 \hat{\text{i}} + 0 \hat{\text{j}} + 4 \hat{k}\right)m⁡$
Work done by the force is given by
$W=F.s$
$=\left(- \hat{\text{i}} + 2 \hat{\text{j}} + 3 \hat{k}\right)\cdot \left(0 \hat{\text{i}} + 0 \hat{\text{j}} + 4 \hat{k}\right)$
$=\left(\right.-1\times 0\left.\right)+\left(\right.2\times 0\left.\right)+\left(\right.3\times 4\left.\right)$
$=0+12$ $\left[\because \hat{\text{i}} \cdot \hat{\text{j}} = \hat{\text{j}} \cdot \hat{\text{j}} = \hat{k} \cdot \hat{k} = 1 \text{and} \hat{\text{i}} \cdot \hat{\text{j}} = \hat{\text{j}} \cdot \hat{k} = \hat{k} \cdot \hat{\text{i}} = 0\right]$
$=12J$