| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Centre of mass of composite shapes |
| Difficulty | Standard +0.3 This is a standard composite shapes centre of mass problem followed by a routine toppling equilibrium calculation. Part (i) requires subtracting areas and applying the standard centre of mass formula (bookwork with arithmetic), while part (ii) involves taking moments about point D with the prism on the point of toppling—a straightforward application of equilibrium conditions. The geometry is clearly defined and the methods are standard M2 techniques with no novel insight required. |
| Spec | 6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
\includegraphics{figure_6}
Fig. 1 shows the cross-section $ABCDE$ through the centre of mass $G$ of a uniform prism. The cross-section consists of a rectangle $ABCF$ from which a triangle $DEF$ has been removed; $AB = 0.6\text{ m}$, $BC = 0.7\text{ m}$ and $DF = EF = 0.3\text{ m}$.
\begin{enumerate}[label=(\roman*)]
\item Show that the distance of $G$ from $BC$ is $0.276\text{ m}$, and find the distance of $G$ from $AB$. [5]
The prism is placed with $CD$ on a rough horizontal surface. A force of magnitude $2\text{ N}$ acting in the plane of the cross-section is applied to the prism. The line of action of the force passes through $G$ and is perpendicular to $DE$ (see Fig. 2). The prism is on the point of toppling about the edge through $D$.
\item Calculate the weight of the prism. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2018 Q6 [8]}}