| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Resultant force on lamina |
| Difficulty | Standard +0.3 This is a standard composite body centre of mass problem followed by a routine toppling equilibrium calculation. Part (i) requires subtracting areas and moments (standard technique), while part (ii) involves taking moments about point D with the prism on the point of toppling (a common mechanics scenario). The calculations are straightforward with no novel insight required, making it slightly easier than average. |
| Spec | 6.04c Composite bodies: centre of mass6.04d Integration: for centre of mass of laminas/solids6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| 6(i) | Area of cross-section of prism = 0.5×0.6 – 0.3×0.3/2 = 0.375 m2 | B1 |
| 0.375y = 0.42×0.6/2 –0.045(0.6 – 0.3/3) | M1 | Take moments about BC |
| y = 0.276 m AG | A1 | |
| 0.375x = 0.42×0.7/2 – 0.045(0.7 – 0.3/3) | M1 | Take moments about AB |
| x = 0.32 m | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 6(ii) | M1 | Attempt to take moments about D |
| 2cos45× (0.7 – 0.32) = 2cos45× (0.3 – 0.276) + W(0.3 – 0.276) | A1 | |
| W = 21(.0) N | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 6:
--- 6(i) ---
6(i) | Area of cross-section of prism = 0.5×0.6 – 0.3×0.3/2 = 0.375 m2 | B1 | Area of cross-section of prism = area of rectangle – area of triangle
0.375y = 0.42×0.6/2 –0.045(0.6 – 0.3/3) | M1 | Take moments about BC
y = 0.276 m AG | A1
0.375x = 0.42×0.7/2 – 0.045(0.7 – 0.3/3) | M1 | Take moments about AB
x = 0.32 m | A1
5
--- 6(ii) ---
6(ii) | M1 | Attempt to take moments about D
2cos45× (0.7 – 0.32) = 2cos45× (0.3 – 0.276) + W(0.3 – 0.276) | A1
W = 21(.0) N | A1
3
Question | Answer | Marks | Guidance\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]
\item 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 $D$.
Calculate the weight of the prism. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2018 Q6 [8]}}