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CAIE A-Level Mathematics 4.1.3 Equilibrium of a Particle

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.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • 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

4.1.3—Forces question 1

[Maximum number: 3]
Figure for Question 4.1.3—Forces question 1 — CAIE A-Level Mathematics A2

Two particles A and B, of masses 3m kg3 m \mathrm{~kg} and 2m kg2 m \mathrm{~kg} respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the edge of a plane. The plane is inclined at an angle θ\theta to the horizontal. A lies on the plane and B hangs vertically, 0.8 m above the floor, which is horizontal. The string between A and the pulley is parallel to a line of greatest slope of the plane (see diagram). Initially A and B are at rest.

Given that the plane is smooth, find the value of θ\theta for which A remains at rest.

It is given instead that the plane is rough, θ=30∘\theta=30^{\circ} and the acceleration of A up the plane is 0.1 m s−20.1 \mathrm{~m} \mathrm{~s}^{-2}.

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