5.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ee5f81bc-1bdb-47a1-81e7-7e3cb8219e91-12_296_1125_246_470}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}

A rough straight ramp is fixed to horizontal ground. The ramp is inclined at an angle $\theta$ to the horizontal, where $\tan \theta = \frac { 5 } { 12 }$

The points $A$ and $B$ are on a line of greatest slope of the ramp, with $A B = 2.5 \mathrm {~m}$ and $B$ above $A$, as shown in Figure 2.

A package of mass 1.5 kg is projected up the ramp from $A$ with speed $U \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and first comes to instantaneous rest at $B$.

The coefficient of friction between the package and the ramp is $\frac { 2 } { 7 }$\\
The package is modelled as a particle.
\begin{enumerate}[label=(\alph*)]
\item Find the work done against friction as the package moves from $A$ to $B$.
\item Use the work-energy principle to find the value of $U$.

After coming to instantaneous rest at $B$, the package slides back down the slope.
\item Use the work-energy principle to find the speed of the package at the instant it returns to $A$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2023 Q5 [10]}}