Theory question 108
DynamicsA particle of mass 400g is moving under the action of two forces; F1 = (35N, 210°) F2 = (35√3N, 300°) and a resistance of 40N. Find the magnitude of the:
(a) resultant of F1 and F2;
(b) resultant force acting on the particle.
Show the model answer
Model answer
Components (east, north) from bearings: F1 = (35 sin 210°, 35 cos 210°) = (−17.5, −30.31)
F2 = (35√3 sin 300°, 35√3 cos 300°) = (−52.5, 30.31)
(a) F1 + F2 = (−70, 0); magnitude 70 N (due west). Check: the forces are at 90°, so √(352 + 3 × 352) = 70 N
(b) The resistance of 40 N opposes the motion: resultant = 70 − 40 = 30 N
Explanation
The bearings differ by 90°, so Pythagoras gives the resultant quickly.