| Exam Board | OCR MEI |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | January |
| Marks | 18 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Folded lamina |
| Difficulty | Standard +0.3 This is a standard M2 centre of mass question with multiple parts involving composite shapes, 3D folding, and equilibrium conditions. While it requires careful bookkeeping across several steps (2D centre of mass, 3D transformation, moments about a line, friction condition), each individual technique is routine for M2. The folding visualization and 3D coordinate work add mild complexity, but the question provides significant scaffolding (showing the answer in part ii, breaking into clear sub-parts). This is slightly easier than average A-level difficulty overall. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04d Integration: for centre of mass of laminas/solids6.04e Rigid body equilibrium: coplanar forces |
A lamina is made from uniform material in the shape shown in Fig. 3.1. BCJA, DZOJ, ZEIO and FGHI are all rectangles. The lengths of the sides are shown in centimetres.
\includegraphics{figure_3}
\begin{enumerate}[label=(\roman*)]
\item Find the coordinates of the centre of mass of the lamina, referred to the axes shown in Fig. 3.1. [5]
\end{enumerate}
The rectangles BCJA and FGHI are folded through 90° about the lines CJ and FI respectively to give the fire-screen shown in Fig. 3.2.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Show that the coordinates of the centre of mass of the fire-screen, referred to the axes shown in Fig. 3.2, are (2.5, 0, 57.5). [4]
\end{enumerate}
The $x$- and $y$-axes are in a horizontal floor. The fire-screen has a weight of 72 N. A horizontal force $P$ N is applied to the fire-screen at the point Z. This force is perpendicular to the line DE in the positive $x$ direction. The fire-screen is on the point of tipping about the line AH.
\begin{enumerate}[label=(\roman*)]
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\item Calculate the value of $P$. [5]
\end{enumerate}
The coefficient of friction between the fire-screen and the floor is $\mu$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{3}
\item For what values of $\mu$ does the fire-screen slide before it tips? [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M2 2008 Q3 [18]}}