Question

two forces 40 Newton and 60 Newton are acting at a point making an angle 60 degree between them find the magnitude and direction of the resultant force

Answer 1

Magnitude (40^2+60^2+2×40×60×cos60)^1/2

Direction is tan 60

Answer 2

Given :

Two forces 40 Newton and 60 Newton are acting at a point making an angle 60 degree between them .

To Find :

The magnitude and direction of the resultant force .

Solution :

We know , magnitude of two force with angle between then  $\theta$ is given by :

$F_{net}=\sqrt{F_1^2+F_2^2+2F_1F_2cos\ \theta}\\\\F_{net}=\sqrt{40^2+60^2+2\times 40\times 60\times cos\ 60^{\circ}}\\\\F_{net }=\sqrt{40^2+60^2+ 40\times 60}\\\\F_{net}= 87.18\ N$

Now , let angle from 40 N force is $\phi$ .

So ,

$cos\ \phi=\dfrac{40}{87.18}\\\\\phi=cos^{-1} 0.46$

Hence , this is the required solution .

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