| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Resultant force on lamina |
| Difficulty | Standard +0.8 This is a composite body centre of mass problem requiring decomposition into rectangle and triangle, calculation of individual centres of mass, and then finding limiting equilibrium conditions (toppling about two different edges). The multi-step nature, spatial reasoning about toppling conditions, and careful moment calculations make this moderately challenging but still within standard M2 scope. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04c Composite bodies: centre of mass |
| Answer | Marks |
|---|---|
| (ii) | ABCF area = 0.64 and CDE = 0.36 |
| Answer | Marks |
|---|---|
| T = 5.5 | B1 |
| Answer | Marks |
|---|---|
| A1 [3] | Both areas correct |
| Answer | Marks | Guidance |
|---|---|---|
| Page 5 | Mark Scheme | Syllabus |
| Cambridge International A Level – October/November 2014 | 9709 | 52 |
Question 4:
--- 4 (i)
(ii) ---
4 (i)
(ii) | ABCF area = 0.64 and CDE = 0.36
0.4 1.8
(0.64 + 0.36)d = 0.64× + 0.36×(0.4 + )
2 3
d = 0.488 m AG
0.488 × 100 = 1.6T
T = 30.5 N
(0.488 – 0.4) × 100 = 1.6T
T = 5.5 | B1
M1
A1
A1
[4]
M1
A1
A1 [3] | Both areas correct
Table of moments idea
All terms correct
Either limiting case
(no turning about A)
(no turning about F)
Page 5 | Mark Scheme | Syllabus | Paper
Cambridge International A Level – October/November 2014 | 9709 | 52\includegraphics{figure_4}
$ABCDEF$ is the cross-section through the centre of mass of a uniform solid prism. $ABCF$ is a rectangle in which $AB = CF = 1.6$ m, and $BC = AF = 0.4$ m. $CDE$ is a triangle in which $CD = 1.8$ m, $CE = 0.4$ m, and angle $DCE = 90°$. The prism stands on a rough horizontal surface. A horizontal force of magnitude $T$ N acts at $B$ in the direction $CB$ (see diagram). The prism is in equilibrium.
\begin{enumerate}[label=(\roman*)]
\item Show that the distance of the centre of mass of the prism from $AB$ is $0.488$ m. [4]
\item Given that the weight of the prism is $100$ N, find the greatest and least possible values of $T$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2014 Q4 [7]}}