Question

For the coplanar concurrent system of forces as shown in the given figure, the system will be

• A. in equilibrium if $|F_3|=10kN$
• B. in equilibrium if $|F_3|=10\sqrt{2}kN$
• C. in equilibrium if $|F_3|=20kN$
• D. will not be in equilibrium whatever be the magnitude of $F_3$

Answer 1

The correct option is D will not be in equilibrium whatever be the magnitude of $F_3$

$F_{3}cos{45}^o=F_2\Rightarrow F_3=20\sqrt{2}kN$

$F_{3}sin{45}^o=F_1\Rightarrow F_3=10\sqrt{2}kN$

Therefore the force will not be in equilibrium for any value of $F_3$
For equilibrium $F_3=\sqrt{F_1^2+F_2^2+2F_1{F}_{2}cos\theta }$
$=10\sqrt{5}kN$
$F_{3}shouldbeatanangletan\theta =\frac{1}{2}fromhorizontal$