Question

If two forces of magnitude 7N and 8N act at 60°, then the resultant will be​

Answer 1

Given : two forces of magnitude 7N and 8N act at 60°

To Find : resultant

Solution:

Two forces A & B acting at angle α

magnitude of Resultant  = √A² + B² + 2ABCosα

two forces of magnitude 7N and 8N act at 60°

Resultant = √(7² + 8²  + 2(7)(8)Cos60°)

= √(49 + 64 + 2(56)(1/2))

= √(113 + 56)

= √(169)

= √(13²)

= 13 N

the resultant will be​  13 N

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Answer 2

Given:

Two forces of magnitude 7N and 8N act at 60°.

To find:

Net resultant force ?

Calculation:

The general expression for addition of two vectors $\vec{A} \:and\:\vec{B}$ is:

$\therefore \: | \vec{R} | = \sqrt{ {A}^{2} + {B}^{2} + 2AB \cos( \theta) }$

Putting the values :

$\implies \: | \vec{R} | = \sqrt{ {7}^{2} + {8}^{2} + \{2 \times 7 \times 8 \times \cos( {60}^{ \circ} ) \}}$

$\implies \: | \vec{R} | = \sqrt{ 49+ 64 + \{112 \times \dfrac{1}{2} \}}$

$\implies \: | \vec{R} | = \sqrt{ 49+ 64 + 56}$

$\implies \: | \vec{R} | = \sqrt{169}$

$\implies \: | \vec{R} | = 13 \: N$

So, net resultant is 13 N.