Problem

5.

Two particles $P$ and $Q$ have masses $0.1\,\mathrm{kg}$ and $0.5\,\mathrm{kg}$ respectively.

The particles are attached to the ends of a light inextensible string.

Particle $P$ is held at rest on a rough horizontal table.

The string lies along the table and passes over a small smooth pulley which is fixed to the edge of the table.

Particle $Q$ is at rest on a smooth plane which is inclined to the horizontal at an angle $\theta$, where $\tan\theta=\frac43$

The string lies in the vertical plane which contains the pulley and a line of greatest slope of the inclined plane, as shown in Figure 2.

Particle $P$ is released from rest with the string taut.

During the first $0.5\,\mathrm{s}$ of the motion $P$ does not reach the pulley and $Q$ moves $0.75\,\mathrm{m}$ down the plane.

(a) Find the tension in the string during the first $0.5\,\mathrm{s}$ of the motion.

(b) Find the coefficient of friction between $P$ and the table.