Edexcel M2 2006 June — Question 4 10 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2006
SessionJune
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCentre of Mass 1
TypeFrame with straight rod/wire components only
DifficultyStandard +0.3 This is a straightforward centre of mass question requiring systematic application of the standard formula for composite bodies. Students set up coordinates, find moments about two axes, then use equilibrium geometry. All steps are routine M2 techniques with no novel insight required, making it slightly easier than average.
Spec6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces

Figure 1 \includegraphics{figure_1} Figure 1 shows four uniform rods joined to form a rigid rectangular framework \(ABCD\), where \(AB = CD = 2a\), and \(BC = AD = 3a\). Each rod has mass \(m\). Particles, of mass \(6m\) and \(2m\), are attached to the framework at points \(C\) and \(D\) respectively.
  1. Find the distance of the centre of mass of the loaded framework from
    1. \(AB\),
    2. \(AD\).
    [7]
The loaded framework is freely suspended from \(B\) and hangs in equilibrium.
  1. Find the angle which \(BC\) makes with the vertical. [3]

Figure 1

\includegraphics{figure_1}

Figure 1 shows four uniform rods joined to form a rigid rectangular framework $ABCD$, where $AB = CD = 2a$, and $BC = AD = 3a$. Each rod has mass $m$. Particles, of mass $6m$ and $2m$, are attached to the framework at points $C$ and $D$ respectively.

\begin{enumerate}[label=(\alph*)]
\item Find the distance of the centre of mass of the loaded framework from
\begin{enumerate}[label=(\roman*)]
\item $AB$,
\item $AD$.
\end{enumerate}
[7]
\end{enumerate}

The loaded framework is freely suspended from $B$ and hangs in equilibrium.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the angle which $BC$ makes with the vertical.
[3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2006 Q4 [10]}}