3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{15f4500a-8eb8-4b5f-896c-de730272a35b-08_396_860_178_641}
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\caption{Figure 3}
\end{figure}
\section*{In this question use \(\boldsymbol { g } = \mathbf { 1 0 m s } \boldsymbol { s } ^ { \mathbf { - 2 } }\).}
A light elastic string has natural length \(a\) metres and modulus of elasticity \(\lambda\) newtons. A particle \(P\) of mass 2 kg is attached to one end of the string. The other end of the string is attached to a fixed point \(A\) on a rough inclined plane. The plane is inclined at angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 3 } { 4 }\)
The point \(B\) on the plane lies below \(A\) on the line of greatest slope of the plane through \(A\) and \(A B = 3 a\) metres, as shown in Figure 3.
The particle \(P\) is held at \(B\) and then released from rest. The particle first comes to instantaneous rest at \(A\).
The coefficient of friction between \(P\) and the plane is \(\frac { 1 } { 4 }\)
- Show that \(\lambda = 24\)
- Find the magnitude of the acceleration of \(P\) at the instant it is released from \(B\).
- Explain why the answer to part (b) is the greatest value of the magnitude of the acceleration of \(P\) as \(P\) moves from \(B\) to \(A\).
[0pt]
[Question 3 Continued]
\section*{4.}