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 $4m$ 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
$W=F.s$
$=\left(-\hat{\text{i}}+2\hat{\text{j}}+3\hat{k}\right)\cdot \left(0\hat{\text{i}}+0\hat{\text{j}}+4\hat{k}\right)$
$=(-1\times 0)+(2\times 0)+(3\times 4)$
$=0+12$ $\left[\because \hat{\text{i}}\cdot \hat{\text{j}}=\hat{\text{j}}\cdot \hat{\text{j}}=\hat{k}\cdot \hat{k}=1\text{and}\hat{\text{i}}\cdot \hat{\text{j}}=\hat{\text{j}}\cdot \hat{k}=\hat{k}\cdot \hat{\text{i}}=0\right]$
$=12J$