CAIE A-Level Mathematics 4.4.4 Connected-Particle Models

CAIE A-Level Mathematics 4.4.4 Connected-Particle Models
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise modelling particles joined by a light inextensible string, using common acceleration and separate or whole-system force equations to determine motion and tension.

How this is tested

  • draw a separate force model for each particle and assign one consistent acceleration direction
  • use equal acceleration magnitudes while the light inextensible string remains taut
  • solve a whole-system equation for acceleration, then substitute into one body equation for tension

Question 2

[Maximum number: 5]

A railway locomotive of mass 240000 kg is towing a coach of mass 36000 kg down a hill inclined at an angle of sin⁡−10.04\sin ^{-1} 0.04 to the horizontal. The driving force produced by the locomotive is 450000 N and there are resistances to motion of 120000 N on the locomotive and 15000 N on the coach. The coupling between the locomotive and the coach is light, rigid and parallel to the hill.

Find the acceleration of the locomotive and the tension in the coupling.