8 An elastic string has one end attached to a point $O$ fixed on a rough horizontal surface. The other end of the string is attached to a particle of mass 2 kg . The elastic string has natural length 0.8 metres and modulus of elasticity 32 newtons.

The particle is pulled so that it is at the point $A$, on the surface, 3 metres from the point $O$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the elastic potential energy when the particle is at the point $A$.
\item The particle is released from rest at the point $A$ and moves in a straight line towards $O$. The particle is next at rest at the point $B$. The distance $A B$ is 5 metres.\\
\includegraphics[max width=\textwidth, alt={}, center]{06c3e260-8167-4616-97d4-0f360a376a0f-6_179_1055_877_497}

Find the frictional force acting on the particle as it moves along the surface.
\item Show that the particle does not remain at rest at the point $B$.
\item The particle next comes to rest at a point $C$ with the string slack.

Find the distance $B C$.
\item Hence, or otherwise, find the total distance travelled by the particle after it is released from the point $A$.
\end{enumerate}

\hfill \mbox{\textit{AQA M2 2012 Q8 [14]}}