| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Framework or multiple rod structures |
| Difficulty | Standard +0.3 This is a standard two-rod framework moments problem requiring center of mass calculation, equilibrium equations (moments about a point and resolving forces), and friction coefficient. While it involves multiple steps across three parts, each step uses routine mechanics techniques without requiring novel insight—slightly easier than average due to the straightforward setup and perpendicular rod configuration. |
| Spec | 3.03u Static equilibrium: on rough surfaces6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| M1 | Table of values or a moment equation | |
| \(0.2 \times 0.1 + 0.3 \times 0 = d(0.2+0.3)\) | A1 | Accept no mention of \(0.3 \times 0\) |
| \(d = 0.04\) m | A1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(4 \times 0.3 = 0.04W\) | M1 | Moments about A |
| \(W = 30\) N | A1ft [2] | ft \(1.2/\text{cv}(d(\text{i}))\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\mu = 4/30\) | M1 | \(4/\text{cv}(W(\text{ii}))\) |
| \(\mu = 0.133\) | A1 [2] | Accept \(2/15\) |
## Question 3:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| | M1 | Table of values or a moment equation |
| $0.2 \times 0.1 + 0.3 \times 0 = d(0.2+0.3)$ | A1 | Accept no mention of $0.3 \times 0$ |
| $d = 0.04$ m | A1 [3] | |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $4 \times 0.3 = 0.04W$ | M1 | Moments about A |
| $W = 30$ N | A1ft [2] | ft $1.2/\text{cv}(d(\text{i}))$ |
### Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\mu = 4/30$ | M1 | $4/\text{cv}(W(\text{ii}))$ |
| $\mu = 0.133$ | A1 [2] | Accept $2/15$ |
**Total: [7]**
---3\\
\includegraphics[max width=\textwidth, alt={}, center]{d6cb7a28-e8d7-4239-b9d3-120a284d7353-2_373_759_1119_694}
A uniform object $A B C$ is formed from two rods $A B$ and $B C$ joined rigidly at right angles at $B$. The rod $A B$ has length 0.3 m and the rod $B C$ has length 0.2 m . The object rests with the end $A$ on a rough horizontal surface and the $\operatorname { rod } A B$ vertical. The object is held in equilibrium by a horizontal force of magnitude 4 N applied at $B$ and acting in the direction $C B$ (see diagram).\\
(i) Find the distance of the centre of mass of the object from $A B$.\\
(ii) Calculate the weight of the object.\\
(iii) Find the least possible value of the coefficient of friction between the surface and the object.
\hfill \mbox{\textit{CAIE M2 2013 Q3 [7]}}