Question 2 - A-Level Maths

The fixed point A is vertically above the fixed point B . A light inextensible string of length 5.4 m has one end attached to A and the other end attached to B. The string passes through a small smooth ring R of mass 0.24 kg , and R is moving at constant angular speed in a horizontal circle. The circle has radius 1.6 m , and \(\mathrm { AR } = 3.4 \mathrm {~m} , \mathrm { RB } = 2.0 \mathrm {~m}\), as shown in Fig. 2 . \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a0df44f-f8f0-44d4-b2f6-70a5314706f9-3_565_504_447_753} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure}
1. Find the tension in the string.
2. Find the angular speed of R .
A particle P of mass 0.3 kg is joined to a fixed point O by a light inextensible string of length 1.8 m . The particle P moves without resistance in part of a vertical circle with centre O and radius 1.8 m . When OP makes an angle of \(25 ^ { \circ }\) with the downward vertical, the tension in the string is 15 N .
1. Find the speed of P when OP makes an angle of \(25 ^ { \circ }\) with the downward vertical.
2. Find the tension in the string when OP makes an angle of \(60 ^ { \circ }\) with the upward vertical.
3. Find the speed of P at the instant when the string becomes slack.