Edexcel M3 2011 January — Question 5

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2011
SessionJanuary
TopicCircular Motion 1

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c150d518-2da6-4f08-90c4-a831a31020f9-09_728_732_157_598} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A small ball \(P\) of mass \(m\) is attached to the ends of two light inextensible strings of length \(l\). The other ends of the strings are attached to fixed points \(A\) and \(B\), where \(A\) is vertically above \(B\). Both strings are taut and \(A P\) is perpendicular to \(B P\) as shown in Figure 3. The system rotates about the line \(A B\) with constant angular speed \(\omega\). The ball moves in a horizontal circle.
  1. Find, in terms of \(m , g , l\) and \(\omega\), the tension in \(A P\) and the tension in \(B P\).
  2. Show that \(\omega ^ { 2 } > \frac { g \sqrt { } 2 } { l }\).