4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e500e20b-9060-4c69-af13-fb97b9a86dfd-07_486_874_223_495}
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\caption{Figure 3}
\end{figure}
One end of a light elastic string, of natural length \(l\) and modulus of elasticity \(3 m g\), is fixed to a point \(A\) on a fixed plane inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 3 } { 5 }\) A small ball of mass \(2 m\) is attached to the free end of the string. The ball is held at a point \(C\) on the plane, where \(C\) is below \(A\) and \(A C = l\) as shown in Figure 3. The string is parallel to a line of greatest slope of the plane. The ball is released from rest. In an initial model the plane is assumed to be smooth.
- Find the distance that the ball moves before first coming to instantaneous rest.
In a refined model the plane is assumed to be rough. The coefficient of friction between the ball and the plane is \(\mu\). The ball first comes to instantaneous rest after moving a distance \(\frac { 2 } { 5 } l\).
- Find the value of \(\mu\).