CAIE A-Level Mathematics 4.1.2 Vector Nature of Force

Practise resolving coplanar forces into components and calculating resultant magnitude, direction or an unknown force.

Exam points

resolve every force into consistent horizontal and vertical components
sum components before calculating resultant magnitude and direction
use a zero or perpendicular resultant component to determine an unknown force

[Maximum number: 3]

Figure for Question 4.1.2—The vector nature of force question 1 — CAIE A-Level Mathematics AS

Coplanar forces, of magnitudes $F \mathrm{~N}, 3 \mathrm{~N}, 6 \mathrm{~N}$ and 4 N , act at a point P, as shown in the diagram.

Given that $\alpha=60$ , and that the resultant of the four forces is in the direction of the 3 N force, find F.

Resolve perpendicular to the direction of the 3 N force:
$4\sin30^\circ+F\sin60^\circ-6=0.$
M1, A1

$F=4.62\text{ N}.$
A1

Accept
$F=\frac{8}{\sqrt3}=\frac{8\sqrt3}{3}.$

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4.1.2—The vector nature of force question 1