CAIE A-Level Mathematics 4.1.3 Equilibrium of a Particle

CAIE A-Level Mathematics 4.1.3 Equilibrium of a Particle
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise applying zero resultant force to particles, rings and connected strings by resolving in suitable directions and solving component equations for forces, tensions or angles.

How this is tested

  • resolve every force along two independent directions and set each component sum to zero
  • solve the simultaneous equilibrium equations for unknown tensions, forces or angles
  • find an equilibrant by reversing the resultant's direction while keeping its magnitude

Question 1

[Maximum number: 5]
Figure for Question 1 — CAIE A-Level Mathematics

Coplanar forces of magnitudes P N,Q N,32 NP \mathrm{~N}, Q \mathrm{~N}, 32 \mathrm{~N} and 21 N act at a point in the directions shown in the diagram. The forces are in equilibrium.

Find the value of P and the value of Q.