| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Toppling and sliding of solids |
| Difficulty | Standard +0.3 This is a standard M2 moments question requiring application of toppling conditions (moment about edge equals zero) and sliding conditions (friction inequality). Part (i) involves straightforward geometry with tan(21°) = r/6, while part (ii) requires comparing friction coefficient to tan(21°). Both parts follow textbook methods with no novel insight required, making it slightly easier than average. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| M1 | Attempt to use trigonometry to form equation for \(r\) | |
| \(r/6 = \tan 21\) | A1 | |
| \(r = 2.3(0)\) | A1 | \(r = 2.30318\ldots\) |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\mu < cv(r)/6\) or \(\mu mg\cos 21 < mg\sin 21\) | M1 | Attempt comparison between weight component and max friction |
| \(\mu < 0.384\) or \(\tan 21\) | A1 | \(\mu < 0.38386\ldots\) or \(0.38333\ldots\) (from 2.3); allow \(\leq\) |
| [2] |
## Question 2:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| | M1 | Attempt to use trigonometry to form equation for $r$ |
| $r/6 = \tan 21$ | A1 | |
| $r = 2.3(0)$ | A1 | $r = 2.30318\ldots$ |
| **[3]** | | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\mu < cv(r)/6$ or $\mu mg\cos 21 < mg\sin 21$ | M1 | Attempt comparison between weight component and max friction |
| $\mu < 0.384$ or $\tan 21$ | A1 | $\mu < 0.38386\ldots$ or $0.38333\ldots$ (from 2.3); allow $\leq$ |
| **[2]** | | |
---2 A uniform solid cylinder of height 12 cm and radius $r \mathrm {~cm}$ is in equilibrium on a rough inclined plane with one of its circular faces in contact with the plane.\\
(i) The cylinder is on the point of toppling when the angle of inclination of the plane to the horizontal is $21 ^ { \circ }$. Find $r$.
The cylinder is now placed on a different inclined plane with one of its circular faces in contact with the plane. This plane is also inclined at $21 ^ { \circ }$ to the horizontal. The coefficient of friction between this plane and the cylinder is $\mu$.\\
(ii) The cylinder slides down this plane but does not topple. Find an inequality for $\mu$.
\hfill \mbox{\textit{OCR M2 2014 Q2 [5]}}