| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Energy methods on slope |
| Difficulty | Standard +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. |
| Spec | 3.03v 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 $A$.
\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]}}