Theory question 117
StaticsCoplanar forces 4N, 8N 6N, 4N and 5N act at a point as shown in the diagram. If the 6N force act in the direction 090°, calculate the (a) magnitude of the resultant force; (b) direction of the resultant force.
Show the model answer
Model answer
Angles measured anticlockwise from the 6N force (east): 6N at 0°, 8N at 55°, 4N at 155°, 4N at −25°, 5N at 205°
East components: 6 + 8 cos 55° − 4 cos 25° + 4 cos 25° − 5 cos 25° = 6.057 N
North components: 8 sin 55° + 4 sin 25° − 4 sin 25° − 5 sin 25° = 4.440 N
(a) |R| = √(6.0572 + 4.4402) ≈ 7.5 N
(b) tan−1(4.440/6.057) ≈ 36.2° north of east, i.e. bearing ≈ 054°
Explanation
Resolve every force along and perpendicular to the 6N force, add, then use Pythagoras and tan⁻¹.