Question

Two forces, F1 and F2, are at an angle Θ. The magnitude of F1 is 2 dynes and that of F2 is 3 dynes. If the magnitude of the resultant of the two forces is 4 dynes, what is the value of Ө?

Answer 1

Answer:

75.5°

Explanation:

If we say F₁ is horizontal (0°), and F₂ is at angle θ, then the components are:

F₁ₓ = 2

F₁ᵧ = 0

F₂ₓ = 3 cos θ

F₂ᵧ = 3 sin θ

So the components of the resultant vector are:

Rₓ = 2 + 3 cos θ

Rᵧ = 3 sin θ

We know the magnitude of R, so using Pythagorean theorem:

4² = (2 + 3 cos θ)² + (3 sin θ)²

16 = 4 + 12 cos θ + 9 cos² θ + 9 sin² θ

16 = 4 + 12 cos θ + 9

3 = 12 cos θ

cos θ = 1/4

θ ≈ 75.5°

Alternatively, you can draw a diagram and use law of cosine to find the internal angle, then subtract from 180 to find θ.