Question

a
To forces of 12N and 5N are acting on
particle, with an angle 60 between them.
Calculate
resultant
forces​

Answer 1

Given :

➳ Two forces of magnitude 12N and 5N are acting at an angle of 60°.

To Find :

➔ Resultant force acting on the particle.

SoluTion :

➝ By traingle law or parallelogram law of vector addition, the magnitude of resultant force F at two forces A and B inclined to each other at angle Φ, is given by

✭ F² = A² + B² + 2AB cosΦ

⇒ F² = A² + B² + 2AB cosΦ

⇒ F² = (12)² + (5)² + 2(12)(5) cos60°

⇒ F² = 144 + 25 + (120 × 1/2)

⇒ F² = 169 + 60

⇒ F² = 229

⇒ F = √229

⇒ F = 15.1 N

Answer 2

Given ,

The forces of 12N and 5N are acting on particle, with an angle 60 between them

We know that ,

The resultant b/w two vectors "a" and "b" is given by

$\boxed{ \sf{Resultant = \sqrt{ {(a)}^{2} + {(b)}^{2} + 2ab \cos( \theta) } }}$

Thus , the resultant force " r " will be :

$\sf \mapsto r = \sqrt{ {(12)}^{2} + {(5)}^{2} + 2 \times 12 \times 5 \times \cos(60) } \\ \\ \sf \mapsto r = \sqrt{144 + 25 + 120 \times \frac{1}{2} } \\ \\ \sf \mapsto r = \sqrt{229} \\ \\ \sf \mapsto r = 15.1 \: \: newton$

Therefore ,

• The resultant force is 15.1 Newton