Question

Two forces of 6 Newton's and 8 Newton's
which are acting at night angles to each other,
will have a resultant of​

Answer 1

Answer:

10 N

Explanation:

As they are at right angle to each other, angle between them is 90°

Using vector addition:

⇒ R = √A² + B² + 2ABcosθ

⇒ R = √6² + 8² + 2(6)(8)cos90°

       = √36 + 64 + 2(6)(8)(0)

       = √100 + 0

       = √100

       = 10

Magnitude on the resultant force is 10 N.

Moreover, tanα = (8/6) = (4/3)

             α = tan⁻¹(4/3)

Direction is defined by tan⁻¹(4/3)

Answer 2

Answer:

Given :-

• Two forces of 6 Newton and 8 Newton which are acting at right angles to each other.

To Find :-

• What is the resultant force.

Solution :-

As we know that :

$\longmapsto \sf\bold{\green{\overrightarrow{R} =\: \overrightarrow{A} + \overrightarrow{B}}}$

Then,

$\leadsto \sf\boxed{\bold{\pink{R =\: \sqrt{{A}^{2} + {B}^{2} + 2ABcos{\theta}}}}}$

Given :

• A = 6 N
• B = 8 N

According to the question by using the formula we get,

$\implies \sf R =\: \sqrt{{(6)}^{2} + {(8)}^{2} + 2(6)(8)cos90^{\circ}}$

$\implies \sf R =\: \sqrt{6 \times 6 + 8 \times 8 + 2 \times 6 \times 8cos90^{\circ}}$

$\implies \sf R =\: \sqrt{36 + 64 + 12 \times 8cos90^{\circ}}$

As we know that, [ cos90° = 0 ]

$\implies \sf R =\: \sqrt{100 + 96 \times 0}$

$\implies \sf R =\: \sqrt{100 + 0}$

$\implies \sf R =\: \sqrt{100}$

$\implies \sf\bold{\red{R =\: 10\: N}}$

$\therefore$ The resultant force is 10 N .