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CAIE A-Level Mathematics AS 4.1.3 Forces Questions

Practise modelling particles in equilibrium by resolving forces and solving simultaneous component equations.

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • use equilibrium conditions to set resultant force components to zero
  • resolve coplanar forces and calculate unknown magnitudes or angles
  • model tensions and other forces acting on particles in equilibrium

CAIE A-Level Mathematics AS 4.1.3 Forces Questions question 1

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Figure for Question CAIE A-Level Mathematics AS 4.1.3 Forces Questions question 1 — CAIE A-Level Mathematics AS

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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