| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Prism or block on inclined plane |
| Difficulty | Challenging +1.2 This is a multi-step mechanics problem requiring moments about the pivot point, resolution of forces, and Hooke's law. While it involves several concepts (equilibrium, toppling condition, elastic strings), the approach is methodical: identify the pivot point B, take moments including the tension component, then use Hooke's law. The geometry is clearly specified and the 30° angles simplify calculations. This is more challenging than routine statics problems but follows standard A-level mechanics procedures without requiring novel insight. |
| Spec | 6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(CP = 0.8\) | B1 | P is the point where the string is attached to the plane |
| \(T = 12 \times (0.8 - 0.4)/0.4\) | M1 | Uses \(T = \lambda x / l\) |
| \(T = 12\text{ N}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| Moment of \(T\) at B \(= 0.4 \times 12\cos30\) | B1\(\checkmark\) | ft for their \(T\) in (i) |
| \(0.4 \times 12\cos30 = 0.2W\cos30 - 0.2W\sin30\) | M1, A1 | Moments about B; Or RHS \(= 0.2\sqrt{2}\cos75W\) or \(W(0.2 - 0.2\tan30)\cos30\) |
| \(W = 56.8\text{ N}\) | A1 |
## Question 5:
### Part (i):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $CP = 0.8$ | B1 | P is the point where the string is attached to the plane |
| $T = 12 \times (0.8 - 0.4)/0.4$ | M1 | Uses $T = \lambda x / l$ |
| $T = 12\text{ N}$ | A1 | |
**Total: 3 marks**
### Part (ii):
| Working/Answer | Mark | Guidance |
|---|---|---|
| Moment of $T$ at B $= 0.4 \times 12\cos30$ | B1$\checkmark$ | ft for their $T$ in (i) |
| $0.4 \times 12\cos30 = 0.2W\cos30 - 0.2W\sin30$ | M1, A1 | Moments about B; Or RHS $= 0.2\sqrt{2}\cos75W$ or $W(0.2 - 0.2\tan30)\cos30$ |
| $W = 56.8\text{ N}$ | A1 | |
**Total: 4 marks**
---5\\
\includegraphics[max width=\textwidth, alt={}, center]{a03ad6c1-b4a3-4007-8d3b-ce289a998a55-3_499_721_715_712}
A uniform solid cube with edges of length 0.4 m rests in equilibrium on a rough plane inclined at an angle of $30 ^ { \circ }$ to the horizontal. $A B C D$ is a cross-section through the centre of mass of the cube, with $A B$ along a line of greatest slope. $B$ lies below the level of $A$. One end of a light elastic string with modulus of elasticity 12 N and natural length 0.4 m is attached to $C$. The other end of the string is attached to a point below the level of $B$ on the same line of greatest slope, such that the string makes an angle of $30 ^ { \circ }$ with the plane (see diagram). The cube is on the point of toppling. Find\\
(i) the tension in the string,\\
(ii) the weight of the cube.
\hfill \mbox{\textit{CAIE M2 2015 Q5 [7]}}