4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b99b3eb0-9bca-42e3-bea9-3b0454a872db-12_483_848_306_589}
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\caption{Figure 3}
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A circus performer has mass \(m\). She is attached to one end of a cable of length \(l\). The other end of the cable is attached to a fixed point \(O\)
Initially she is held at rest at point \(A\) with the cable taut and at an angle of \(30 ^ { \circ }\) below the horizontal, as shown in Figure 3.
The circus performer is released from \(A\) and she moves on a vertical circular path with centre \(O\)
The circus performer is modelled as a particle and the cable is modelled as light and inextensible.
- Find, in terms of \(m\) and \(g\), the tension in the cable at the instant immediately after the circus performer is released.
- Show that, during the motion following her release, the greatest tension in the cable is 4 times the least tension in the cable.