Theory question 108
StaticsForces F1 (18 N, 330°), F2 (10 N, 090°) and F3 (25 N, 180°) act on a body at rest. Find, correct to one decimal place, the magnitude and direction of the resultant force.
Show the model answer
Model answer
Components (east, north) = (F sin θ, F cos θ):
F₁ = (−9, 15.59); F₂ = (10, 0); F₃ = (0, −25).
Resultant = (1, −9.41); magnitude ≈ 9.5 N.
Direction: bearing 180° − tan⁻¹(1/9.41) ≈ 173.9°.
Explanation
Resolve each force into east and north components.