The resultant of two forces acting at an angle of 120^ is 10 ~kg - W and is perpendicular to one of the forces. That force is

Step-by-step solution

Let the two forces be F₁ and F₂ . The angle between them is = 120^ . The resultant R = 10 kg-W is perpendicular to F₁ . The formula for the angle that the resultant makes with F₁ is given by = F₂ F₁ + F₂ . Since the resultant is perpendicular to F₁ , = 90^ , which implies 90^ = . This occurs when the denominator is zero: F₁ + F₂ 120^ = 0 F₁ + F₂ (-0.5) = 0 F₁ = 0.5 F₂ F₂ = 2 F₁ . The magnitude of the resultant R is given by R^2 = F₁^2 + F₂^2 + 2 F₁ F₂ 120^ . Substituting R = 10 and F₂ = 2 F₁ : 10^2 = F₁^2 + (2 F₁)^