Edexcel M1 2012 January — Question 4 9 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2012
SessionJanuary
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeBeam on point of tilting
DifficultyStandard +0.3 This is a standard M1 moments question requiring taking moments about a pivot point to find the center of mass position, then applying equilibrium conditions. The setup is straightforward with clear geometry, and part (a) is a 'show that' which guides students to the answer. Part (b) requires resolving forces and taking moments again, but follows a predictable pattern typical of textbook exercises. Slightly easier than average due to the guided nature and standard approach.
Spec3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{724254f3-3a6a-4820-b3a1-979458e24437-05_241_794_219_575} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A non-uniform \(\operatorname { rod } A B\), of mass \(m\) and length \(5 d\), rests horizontally in equilibrium on two supports at \(C\) and \(D\), where \(A C = D B = d\), as shown in Figure 1. The centre of mass of the rod is at the point \(G\). A particle of mass \(\frac { 5 } { 2 } m\) is placed on the rod at \(B\) and the rod is on the point of tipping about \(D\).
  1. Show that \(G D = \frac { 5 } { 2 } d\). The particle is moved from \(B\) to the mid-point of the rod and the rod remains in equilibrium.
  2. Find the magnitude of the normal reaction between the support at \(D\) and the rod.

4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{724254f3-3a6a-4820-b3a1-979458e24437-05_241_794_219_575}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

A non-uniform $\operatorname { rod } A B$, of mass $m$ and length $5 d$, rests horizontally in equilibrium on two supports at $C$ and $D$, where $A C = D B = d$, as shown in Figure 1. The centre of mass of the rod is at the point $G$. A particle of mass $\frac { 5 } { 2 } m$ is placed on the rod at $B$ and the rod is on the point of tipping about $D$.
\begin{enumerate}[label=(\alph*)]
\item Show that $G D = \frac { 5 } { 2 } d$.

The particle is moved from $B$ to the mid-point of the rod and the rod remains in equilibrium.
\item Find the magnitude of the normal reaction between the support at $D$ and the rod.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2012 Q4 [9]}}