Edexcel M2 2004 January — Question 3 9 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2004
SessionJanuary
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAdvanced work-energy problems
TypeRough inclined plane work-energy
DifficultyStandard +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.
Spec3.03r 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. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{fe64e6f1-e36b-465d-a41c-ac834439623b-3_435_832_379_571}
\end{figure} 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,
  1. 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,
  2. find the coefficient of friction between \(P\) and the plane.

3.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
  \includegraphics[alt={},max width=\textwidth]{fe64e6f1-e36b-465d-a41c-ac834439623b-3_435_832_379_571}
\end{center}
\end{figure}

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]}}