Edexcel M2 2006 June — Question 7 12 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2006
SessionJune
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMotion on a slope
TypeEnergy methods on slope
DifficultyStandard +0.3 This is a standard M2 mechanics question on inclined plane motion using work-energy principles. It requires routine application of friction forces, resolving perpendicular to the plane for normal reaction, calculating work done against friction and gravity, and applying energy conservation. While multi-part with 12 marks total, each step follows a predictable template with no novel problem-solving required—slightly easier than average A-level maths.
Spec3.03v Motion on rough surface: including inclined planes6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.02i Conservation of energy: mechanical energy principle

A particle \(P\) has mass 4 kg. It is projected from a point \(A\) up a line of greatest slope of a rough plane inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac{3}{4}\). The coefficient of friction between \(P\) and the plane is \(\frac{2}{5}\). The particle comes to rest instantaneously at the point \(B\) on the plane, where \(AB = 2.5\) m. It then moves back down the plane to \(A\).
  1. Find the work done by friction as \(P\) moves from \(A\) to \(B\). [4]
  1. Using the work-energy principle, find the speed with which \(P\) is projected from \(A\). [4]
  1. Find the speed of \(P\) when it returns to \(A\). [4]

A particle $P$ has mass 4 kg. It is projected from a point $A$ up a line of greatest slope of a rough plane inclined at an angle $\alpha$ to the horizontal, where $\tan \alpha = \frac{3}{4}$. The coefficient of friction between $P$ and the plane is $\frac{2}{5}$. The particle comes to rest instantaneously at the point $B$ on the plane, where $AB = 2.5$ m. It then moves back down the plane to $A$.

\begin{enumerate}[label=(\alph*)]
\item Find the work done by friction as $P$ moves from $A$ to $B$.
[4]
\end{enumerate}

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Using the work-energy principle, find the speed with which $P$ is projected from $A$.
[4]
\end{enumerate}

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the speed of $P$ when it returns to $A$.
[4]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2006 Q7 [12]}}