Question

Two forces 20N and 5N are acting at an angle 120 between them .find the resultant force in magnitude and direction

Answer 1

$\bold{\varnothing=\tan ^{-1} \frac{\sqrt{3}}{7}}$ is the resultant force of the given.

Explanation:

The resultant of the two forces which is acting on a same point where it is maximum, when all the forces are acting in a same direction and also having minimum magnitude when they are operating in an opposite direction.

If two forces are acting in a same direction, when the direction of angle between the two forces becomes 0. In this given case, the resultant force is the sum of two forces which its direction is same as that of the two independent forces.

Given:

The magnitude of two forces is 20 N and 5 N

$\mathrm{R}=\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB} \cos \theta}$

$=\sqrt{(2)^{2}+(5)^{2}+2 \times 20 \times 5 \times \cos 120}$

  $=\sqrt{325 \mathrm{N}}$

$\tan \varnothing=\frac{A \sin \theta}{A+B \cos \theta}(Ø is the angle of R ⃗ with  A ⃗ )$

$=\frac{\left(5 \times \sqrt{\frac{3}{2}}\right)}{20-5 \times \frac{1}{2}}=\frac{\sqrt{3}}{7}$

$\varnothing=\tan ^{-1} \frac{\sqrt{3}}{7}$.

Answer 2

Explanation:

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