| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2004 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Rough inclined plane work-energy |
| Difficulty | Standard +0.3 This is a standard M2 work-energy question with two straightforward parts: (a) applies conservation of energy on a smooth plane (routine calculation), and (b) uses work-energy principle to find coefficient of friction given speeds. Both parts follow textbook methods with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03r Friction: concept and vector form3.03v Motion on rough surface: including inclined planes6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.02c Work by variable force: using integration |
3.
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\caption{Figure 1}
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A particle $P$ of mass 2 kg is projected from a point $A$ up a line of greatest slope $A B$ of a fixed plane. The plane is inclined at an angle of $30 ^ { \circ }$ to the horizontal and $A B = 3 \mathrm {~m}$ with $B$ above $A$, as shown in Fig. 1. The speed of $P$ at $A$ is $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
Assuming the plane is smooth,
\begin{enumerate}[label=(\alph*)]
\item find the speed of $P$ at $B$.
The plane is now assumed to be rough. At $A$ the speed of $P$ is $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and at $B$ the speed of $P$ is $7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. By using the work-energy principle, or otherwise,
\item find the coefficient of friction between $P$ and the plane.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2004 Q3 [9]}}