Question

16. The sum of three forces Fi = 100N, F2 = 80N and F3 = 60N
acting on a particle is zero. The angle between vector F1 and vector F2 is :​

Answer 1

Given : The sum of three forces F₁ = 100N , F₂ = 80 N and F₃ = 60 N acting on a particle is zero.

To find : The angle between F₁ and F₂

solution : let angle between F₁ and F₂ is θ.

so resultant of F₁ and F₂ , F = √{F₁² + F₂² + 2F₁.F₂cosθ}

F = √{(100)² + (80)² + 2(100)(80)cosθ}

a/c to question,

The sum of three forces acting on a particle is zero.

so, resultant of F₁ and F₂ = F₃

now , F₃ = √{(100)² + (80)² + 2(100)(80)cosθ}

⇒60² = (100)² + (80)² + 2(100)(80)cosθ

⇒3600 = 10000 + 6400 + 16000 cosθ

⇒-12800 = 16000 cosθ

⇒cosθ = -12800/16000 = -128/160 = -4/5

⇒θ = cos¯¹ (-4/5) = 143.1°

Therefore the angle between F₁ and F₂ is 143.1°