2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0567d068-e23c-446e-9e11-f0c292972093-06_531_837_258_632}
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\caption{Figure 2}
\end{figure}
One end of a string of length \(3 a\) is attached to a point \(A\) and the other end is attached to a point \(B\) on a smooth horizontal table. The point \(B\) is vertically below \(A\) with \(A B = a \sqrt { 3 }\) A small smooth bead, \(P\), of mass \(m\) is threaded on to the string. The bead \(P\) moves on the table in a horizontal circle, with centre \(B\), with constant speed \(U\). Both portions, \(A P\) and \(B P\), of the string are taut, as shown in Figure 2.
The string is modelled as being light and inextensible and the bead is modelled as a particle.
- Show that \(A P = 2 a\)
- Find, in terms of \(m , U\) and \(a\), the tension in the string.
- Show that \(U ^ { 2 } < a g \sqrt { 3 }\)
- Describe what would happen if \(U ^ { 2 } > a g \sqrt { 3 }\)
- State briefly how the tension in the string would be affected if the string were not modelled as being light.