6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{e6e37d85-f8de-490a-82a9-8a3c16e2fdd0-16_273_819_260_566}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

Two particles, $A$ and $B$, of mass 2 kg and 3 kg respectively, are connected by a light inextensible string. Particle $A$ is held at rest at the point $X$ on a fixed rough ramp that is inclined at an angle $\theta$ to the horizontal, where $\tan \theta = \frac { 5 } { 12 }$. The string passes over a small smooth pulley $P$ that is fixed at the top of the ramp. Particle $B$ hangs vertically below $P$, 2 m above the ground, as shown in Figure 4.

The particles are released from rest with the string taut so that $A$ moves up the ramp and the section of the string from $A$ to $P$ is parallel to a line of greatest slope of the ramp. The coefficient of friction between $A$ and the ramp is $\frac { 3 } { 8 }$

Air resistance is ignored.
\begin{enumerate}[label=(\alph*)]
\item Find the potential energy lost by the system as $A$ moves 2 m up the ramp.
\item Find the work done against friction as $A$ moves 2 m up the ramp.

When $B$ hits the ground, $B$ is brought to rest by the impact and does not rebound and $A$ continues to move up the ramp.
\item Use the work-energy principle to find the speed of $B$ at the instant before it hits the ground.

Particle $A$ comes to instantaneous rest at the point $Y$ on the ramp, where $X Y = ( 2 + d ) \mathrm { m }$.
\item Use the work-energy principle to find the value of $d$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2021 Q6 [15]}}