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Q.
There are four forces acting at a point $P$ produced by strings as shown in figure, which is at rest. The forces $F_{1}$ and $F_{2}($ in $N )$ are
Laws of Motion
Solution:
On resolving forces into rectangular components in the given figure as shown below
At equilibrium, $\Sigma F_{x}=0$ and $\Sigma F_{y}=0$
$\Rightarrow 2 \cos 45^{\circ}+\sin 45^{\circ}=F_{2}$
and $ 2 \sin 45^{\circ}=F_{1}+\cos 45^{\circ}$
$\Rightarrow F_{1}=2 \sin 45^{\circ}-\cos 45^{\circ}$
$=\sqrt{2}-\frac{1}{\sqrt{2}}$
$=\frac{2-1}{\sqrt{2}}=\frac{1}{\sqrt{2}}$
$=0.707\, N \simeq 0.7\, N$
and $F_{2} =\sqrt{2}+\frac{1}{\sqrt{2}}$
$=\frac{2+1}{\sqrt{2}} N =\frac{3}{\sqrt{2}}$
$=2.121\, N \simeq 2.1\, N$
