Question

if the resultant of two forces 6n and 8n is 12n find the angle between them?

Answer 1

Answer:

cos⁻¹ ( 11 / 24 )

Explanation:

Given :

F₁ = 6 N

F₂ = 8 N

Resultant Force = 12 N

We have to find angle :

We know :

R = √ ( F₁² + F₂² + 2 F₁ F₂ cos Ф )

Squaring on both side :

R² = ( F₁² + F₂² + 2 F₁ F₂ cos Ф )

Putting value here we get :

12² = 6² + 8² + 2 . 6 . 8 . cos Ф

144 - 100 = 96 cos Ф

cos Ф = 44 / 96

cos  Ф = 11 /  24

Ф = cos⁻¹ ( 11 / 24 )

Therefore , angle between them is cos⁻¹ ( 11 / 24 ).