Question

Figure shows three forces applied to a trunk that moves leftward by $3$ m over a smooth floor. The force magnitudes are $F_1=5N,F_2=9N,$ and $F_3=3N$. The net work done on the trunk by the three forces

• A. $1.50\text{J}$
• B. $2.40\text{J}$
• C. $3.00\text{J}$
• D. $6.00\text{J}$

Answer 1

The correct option is A $1.50\text{J}$

$\overrightarrow{F}=-5\hat{i}+9cos{60}^{\circ }\hat{i}+9sin{60}^{\circ }\hat{j}-3\hat{j}$
$\overrightarrow{F}=-5\hat{i}+\frac{9}{2}\hat{i}+\frac{9\sqrt{3}}{2}\hat{j}-3\hat{j}$
$\overrightarrow{F}=-\frac{\hat{i}}{2}+(\frac{9\sqrt{3}}{2}-3)\hat{j}$
$\overrightarrow{s}=-3\hat{i}.$
$W=\overrightarrow{F}.\overrightarrow{s}=[-\frac{\hat{i}}{2}+(\frac{9\sqrt{3}}{2}-3)\hat{j}].(-3\hat{i})=1.5J.$