Theory question 114
StaticsA particle of weight 12 N lying on a horizontal ground is acted upon by forces F1 = (10 N, 090°), F2 = (16 N, 180°), F3 = (7 N, 030°) and F4 = (12 N, 300°). (a) Express all the forces acting on the particle as column vectors. (b) Find, correct to two decimal places, the magnitude of the (i) resultant force; (ii) acceleration with which the particle starts to move. [Take g = 10 ms−2]
Show the model answer
Model answer
Bearing θ gives (F sin θ, F cos θ) (east, north):
(a) F₁ = (10, 0); F₂ = (0, −16); F₃ = (3.50, 6.06); F₄ = (−10.39, 6.00).
(b)(i) Resultant = (3.11, −3.94); magnitude = √(3.108² + 3.938²) = √25.16 ≈ 5.02 N.
(ii) Mass = 12/10 = 1.2 kg; a = 5.016/1.2 ≈ 4.18 ms⁻².
Explanation
Convert each bearing into east and north components, then add.