CAIE A-Level Mathematics AS 4.4.4 Connected Particle Models Questions

Practise modelling connected particles, strings, tow-bars and coupled vehicles with Newton’s laws.

Exam points

set up equations of motion for connected particles
relate acceleration and tension through inextensible strings or couplings
solve coupled-system problems involving friction, slopes and engines

[Maximum number: 5]

Figure for Question CAIE A-Level Mathematics AS 4.4.4 Connected Particle Models Questions question 1 — CAIE A-Level Mathematics AS

Two particles A and B, of masses $3 m \mathrm{~kg}$ and $2 m \mathrm{~kg}$ 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 $\theta$ 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.

Show that the coefficient of friction between A and the plane is $\frac{1}{10} \sqrt{3}$ .

$R=3 m g \cos 30$
Use of $F=\mu R$ $2 m g-T=0.1 \times 2 m$ OR $T-3 m g \sin 30-\mu \times 3 m g \cos 30=0.1 \times 3 m$ $2 m g-0.2 m-3 m g \sin 30-\mu \times 3 m g \cos 30=0.1 \times 3 m$ $\mu=\frac{\sqrt{3}}{10}$

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CAIE A-Level Mathematics AS 4.4.4 Connected Particle Models Questions question 1