There are four forces acting at a point $P$ produced by strings as shown in figure. Which is at rest ? Find the forces $F_1$ and $F_2$.
There are four forces acting at a point $P$ produced by strings as shown in figure. Which is at rest ? Find the forces $F_1$ and $F_2$.
Let $\mathrm{F}_{3}=1 \mathrm{~N}$ (given)
$\mathrm{F}_{4}=2 \mathrm{~N}$ (given)
String is at rest,
$\Sigma \overrightarrow{\mathrm{F}}=0$
$\Sigma \mathrm{F}_{x}=0$
$\mathrm{~F}_{2}+1 \cos 45-2 \cos 45=0$
$\mathrm{~F}_{2}+\cos 45(1-2)=0$
$\mathrm{~F}_{2}+\frac{1}{\sqrt{2}}(-1)=0$
$\mathrm{~F}_{2}=\frac{1}{\sqrt{2}} \mathrm{~N}$
$\Sigma \mathrm{F}_{y}=0$
$1 \sin 45+2 \sin 45-\mathrm{F}_{2}=0$
$3 \sin 45-\mathrm{F}_{2}=0$
$\mathrm{~F}_{2}=3 \sin 45$
$=\frac{3}{\sqrt{2}}$
$=2.121 \mathrm{~N}$
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