CAIE A-Level Mathematics 4.1.6 Limiting Friction and Equilibrium

CAIE A-Level Mathematics 4.1.6 Limiting Friction and Equilibrium
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise modelling a particle about to slip, resolving to find the normal reaction and using F = μR with the correct impending-motion direction to solve coefficients or angle…

How this is tested

  • infer the friction direction opposite the stated or impending relative motion
  • resolve perpendicular to the contact surface to calculate the normal reaction R
  • set F = μR only at limiting equilibrium and solve the remaining force or angle equation

Question 5

[Maximum number: 6]
Figure for Question 5 — CAIE A-Level Mathematics

A particle P of mass m kgm \mathrm{~kg} is in equilibrium on a rough plane inclined at an angle θ∘\theta^{\circ} to the horizontal. The equilibrium of P is maintained by a force of magnitude 8mg N8 m g \mathrm{~N} making an angle θ∘\theta^{\circ} with a line of greatest slope (see diagram). The coefficient of friction between P and the plane is 0.5 and P is on the point of slipping down the plane.

Find the value of θ\theta.