5
\includegraphics[max width=\textwidth, alt={}, center]{4c8f0d10-ea1e-4aee-870d-71a52dd948ed-03_697_579_1238_781} Two small rings \(A\) and \(B\) are attached to opposite ends of a light inextensible string. The rings are threaded on a rough wire which is fixed vertically. \(A\) is above \(B\). A horizontal force is applied to a point \(P\) of the string. Both parts \(A P\) and \(B P\) of the string are taut. The system is in equilibrium with angle \(B A P = \alpha\) and angle \(A B P = \beta\) (see diagram). The weight of \(A\) is 2 N and the tensions in the parts \(A P\) and \(B P\) of the string are 7 N and \(T \mathrm {~N}\) respectively. It is given that \(\cos \alpha = 0.28\) and \(\sin \alpha = 0.96\), and that \(A\) is in limiting equilibrium.

1. Find the coefficient of friction between the wire and the ring \(A\).
2. By considering the forces acting at \(P\), show that \(T \cos \beta = 1.96\).
3. Given that there is no frictional force acting on \(B\), find the mass of \(B\). \section*{June 2005}