Question

Forces 4 N, 4 N and 3 N are in equilibrium. Find the angle between the two 4 N forces.

Answer 1

Given :

Forces 4N, 4N and 3N are in equilibrium

To find :

Angle between the two 4N forces

Solution :

• Since the forces are in equilibrium, they can be represented by the sides of triangle taken in order

• Applying cosine rule for α angle i.e angle between two 4N forces.

Also,

a = 4, b = 4 and c = 3

• Cosine rule is given by,

$cos \: \alpha = {a}^{2} + {b}^{2} - {c}^{2} \div 2ab$

cos α = 4^2 + 4^2 - 3^2 / 2×4×4

= 16 + 16 - 9 / 32

= 32 - 9 / 32

= 23 / 32

α = cos^-1 ( 23/32)

α = cos^-1 ( 0.718 )

Answer 2

Given :

• Forces ar 4N, 4N and 3N.

To find :

• Angle netween the forces of 4N.

Solution :

• Refer the diagram attached.
• As the forces are in equilibrium, the can be represented by a triangle.
• Let the angle between the two forces of 4 N be θ .
• Then, in the triangle, the angle between the two forces will be 180-θ.
• According to cosine rule,

        3² = 4² + 4² - 2×4×4×cos(180-θ)

        9 = 16 + 16 - 32cos(180-θ)

        cos(180-θ) = (32-9)/32

        cos(180-θ) = 0.71875

        (180-θ) = cos(0.71875)

        180 - θ ≈ 1°

          ∴ θ = 179°

Answer : The angle between the 4 N forces will be 179°.