| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2019 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Lamina hinged at point with string support |
| Difficulty | Standard +0.3 This is a standard mechanics question on moments with a triangular lamina. Part (i) requires recall of the centroid formula (1/3 from each side), part (ii) is a straightforward equilibrium problem using tan θ, and part (iii) involves taking moments about B with a given force. All steps are routine applications of standard techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04b Find centre of mass: using symmetry |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| From \(AB = 0.2\) | B1 | |
| From \(BC = 0.1\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\tan\theta = \frac{0.1}{0.2}\) | M1 | \(\theta\) is the angle between \(AB\) and the horizontal |
| \(\theta = 26.6°\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(12\cos 26.6 \times 0.3 = W \times 0.2\) | M1A1 | Take moments about \(B\). (\(W\) is the weight of the lamina) |
| \(W = 16.1 \text{ N}\) | A1 |
## Question 6(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| From $AB = 0.2$ | B1 | |
| From $BC = 0.1$ | B1 | |
---
## Question 6(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\tan\theta = \frac{0.1}{0.2}$ | M1 | $\theta$ is the angle between $AB$ and the horizontal |
| $\theta = 26.6°$ | A1 | |
---
## Question 6(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $12\cos 26.6 \times 0.3 = W \times 0.2$ | M1A1 | Take moments about $B$. ($W$ is the weight of the lamina) |
| $W = 16.1 \text{ N}$ | A1 | |
---6\\
$A B C$ is a uniform lamina in the form of a triangle with $A B = 0.3 \mathrm {~m} , B C = 0.6 \mathrm {~m}$ and a right angle at $B$ (see diagram).\\
(i) State the distances of the centre of mass of the lamina from $A B$ and from $B C$.
Distance from $A B$\\
Distance from $B C$ $\_\_\_\_$\\
The lamina is freely suspended at $B$ and hangs in equilibrium.\\
(ii) Find the angle between $A B$ and the horizontal.\\
A force of magnitude 12 N is applied along the edge $A C$ of the lamina in the direction from $A$ towards $C$. The lamina, still suspended at $B$, is now in equilibrium with $A B$ vertical.\\
(iii) Calculate the weight of the lamina.\\
\hfill \mbox{\textit{CAIE M2 2019 Q6 [7]}}