Edexcel M2 2015 June — Question 4 11 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2015
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicHooke's law and elastic energy
TypeParticle on inclined plane with friction
DifficultyStandard +0.3 This is a standard M2 work-energy question with friction on an inclined plane. Part (a) requires setting up work-energy equation with friction, weight component, and kinetic energy—routine but multi-step. Part (b) requires recognizing friction reverses direction on descent. Slightly above average due to the two-part nature and careful sign handling, but follows standard M2 templates.
Spec3.03v Motion on rough surface: including inclined planes6.02i Conservation of energy: mechanical energy principle

\includegraphics{figure_1} Figure 1 A particle \(P\) of mass 6.5 kg is projected up a fixed rough plane with initial speed 6 m s\(^{-1}\) from a point \(X\) on the plane, as shown in Figure 1. The particle moves up the plane along the line of greatest slope through \(X\) and comes to instantaneous rest at the point \(Y\), where \(XY = d\) metres. The plane is inclined at an angle \(\theta\) to the horizontal, where \(\tan \theta = \frac{5}{12}\). The coefficient of friction between \(P\) and the plane is \(\frac{1}{3}\).
  1. Use the work-energy principle to show that, to 2 significant figures, \(d = 2.7\) [7]
After coming to rest at \(Y\), the particle \(P\) slides back down the plane.
  1. Find the speed of \(P\) as it passes through \(X\). [4]

\includegraphics{figure_1}

Figure 1

A particle $P$ of mass 6.5 kg is projected up a fixed rough plane with initial speed 6 m s$^{-1}$ from a point $X$ on the plane, as shown in Figure 1. The particle moves up the plane along the line of greatest slope through $X$ and comes to instantaneous rest at the point $Y$, where $XY = d$ metres. The plane is inclined at an angle $\theta$ to the horizontal, where $\tan \theta = \frac{5}{12}$.

The coefficient of friction between $P$ and the plane is $\frac{1}{3}$.

\begin{enumerate}[label=(\alph*)]
\item Use the work-energy principle to show that, to 2 significant figures, $d = 2.7$ [7]
\end{enumerate}

After coming to rest at $Y$, the particle $P$ slides back down the plane.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the speed of $P$ as it passes through $X$. [4]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2015 Q4 [11]}}