Question

The resultant of two forces F₁ = 400 N and F₂ = 260 N acting at point A is 520 N. Determine the angle between the two forces and the angle between the resultant and force F₁.

Answer 1

Let ABC be the triangle of forces as shown in. θ be the angle between F₁ and F₂, and α be the angle between resultant and F₁ Using the relation

R = \(\sqrt{F_1^2+F_2^2+2F_1F_2\,cos\,\theta}\)

520² = 400² + 260² + 2 × 400 × 260 × cos θ

∴ cos θ = 0.20577 

∴ θ = 78.13° 

Noting that 

R sin α = F₂ sin θ

sin α = \(\cfrac{260 \,sin \,78.13 °}{520}\) = 0.489

∴ α = 29.29°