Edexcel M1 2017 January — Question 6 14 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2017
SessionJanuary
Marks14
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMotion on a slope
TypeHorizontal force on slope
DifficultyStandard +0.3 This is a standard two-part M1 mechanics question involving motion on a rough inclined plane. Part (a) requires resolving forces, finding acceleration, and using kinematics (SUVAT) - routine for M1. Part (b) involves resolving a horizontal force and applying limiting friction in the opposite direction - slightly less routine but still a standard textbook exercise. The multi-step nature and need to handle friction in both directions makes it slightly above average difficulty for M1, but it requires no novel insight.
Spec3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-10_609_1013_118_456} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A particle \(P\) of mass 4 kg is held at rest at the point \(A\) on a rough plane which is inclined at \(30 ^ { \circ }\) to the horizontal. The point \(B\) lies on the line of greatest slope of the plane that passes through \(A\). The point \(B\) is 5 m down the plane from \(A\), as shown in Figure 3. The coefficient of friction between the plane and \(P\) is 0.3 The particle is released from rest at \(A\) and slides down the plane.
  1. Find the speed of \(P\) at the instant it reaches \(B\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-10_478_1011_1343_456} \captionsetup{labelformat=empty} \caption{Figure 4}
    \end{figure} The particle is now returned to \(A\) and is held in equilibrium by a horizontal force of magnitude \(H\) newtons, as shown in Figure 4. The line of action of the force lies in the vertical plane containing the line of greatest slope of the plane through \(A\). The particle is on the point of moving up the plane.
  2. Find the value of \(H\).

6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-10_609_1013_118_456}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

A particle $P$ of mass 4 kg is held at rest at the point $A$ on a rough plane which is inclined at $30 ^ { \circ }$ to the horizontal. The point $B$ lies on the line of greatest slope of the plane that passes through $A$. The point $B$ is 5 m down the plane from $A$, as shown in Figure 3. The coefficient of friction between the plane and $P$ is 0.3

The particle is released from rest at $A$ and slides down the plane.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $P$ at the instant it reaches $B$.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-10_478_1011_1343_456}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

The particle is now returned to $A$ and is held in equilibrium by a horizontal force of magnitude $H$ newtons, as shown in Figure 4. The line of action of the force lies in the vertical plane containing the line of greatest slope of the plane through $A$. The particle is on the point of moving up the plane.
\item Find the value of $H$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2017 Q6 [14]}}