Question

What is the resultant of three coplanar forces $300\text{N}$ at $0^o$, $400\text{N}$ at ${30}^{\circ }$ and $400\text{N}$ at ${150}^{\circ }$ with $x-$ axis?

• A. $500\text{N}$
• B. $700\text{N}$
• C. $1100\text{N}$
• D. $300\text{N}$

Answer 1

The correct option is A $500\text{N}$

By resolving all the vectors
$\overrightarrow{F_1}=300\hat{i},\overrightarrow{F_2}=400\cos {30}^{\circ }\hat{i}+400\sin {30}^{\circ }\hat{j}$
$=400\frac{\sqrt{3}}{2}\hat{i}+\frac{400}{2}\hat{j}$
$\overrightarrow{F_3}=-400\cos {30}^{\circ }\hat{i}+400\sin {30}^{\circ }\hat{j}$
$=-400\frac{\sqrt{3}}{2}\hat{i}+\frac{400}{2}\hat{j}$
$\overrightarrow{R}=\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}$
$=300\hat{i}+200\sqrt{3}\hat{i}+200\hat{j}-200\sqrt{3}\hat{i}+200\hat{j}$
$=300\hat{i}+400\hat{j}|\overrightarrow{R}|=\sqrt{{300}^2+{400}^2}$
$|\overrightarrow{R}|=500\text{N}$