Question

two force of 60N and 40N are inclined to each other at an angle of 60°. find the magnitude and direction of their resultant .​

Answer 1

Given :-

Force 1 = 60 N

Force 2 = 40 N

The two forces are inclined at an angle = 60°

To Find :-

Magnitude and direction of the resultant.

Solution :-

We know that,

• r = Resultant
• a = Force 1
• b = Force 2

Resultant of two forces is given by,

$\underline{\boxed{\sf Resultant = \sqrt{A^2+B^2+2AB \ cos \ \theta}}}$

Given that,

Force 1 (a) = 60 N

Force 2 (b) = 40 N

Substituting their values,

⇒ r = √60² + 40² + 2400

⇒ r = √3600 + 1600 + 2400

⇒ r = √7600

⇒ r = 87.18 N

Finding the direction,

⇒ cos ω = 60/87.18

⇒ cos ω = 0.69

⇒ ω = cos⁻¹ 0.69

Therefore, the magnitude and direction of their resultant is cos⁻¹ 0.69.