| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2012 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod or block on rough surface in limiting equilibrium (no wall) |
| Difficulty | Standard +0.3 This is a standard mechanics problem requiring moments about a point, resolution of forces, and friction in limiting equilibrium. While it involves multiple steps (taking moments, resolving horizontally and vertically, finding coefficient of friction), these are routine techniques for M2 level. The setup is clearly defined with no geometric complications, making it slightly easier than average for A-level mechanics. |
| Spec | 3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| \(6 \times 0.4\cos60 = 0.8 P\cos45\) | M1 | Takes moments about \(B\) |
| \(P\) is the force at \(A\) | A1 | |
| \(P = 2.12\text{N}\) | A1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = P\sin75\) (F is friction force at \(B\)) | B1 | Must use correct angle \((\cos15)\) |
| \(R = 6 + P\cos75\) (R is normal reaction at \(B\)) | B1 | Must use correct angle \((\sin15)\) |
| \(\mu = (2.12\sin75)/(6 + 2.12\cos75)\) | M1 | |
| \(\mu = 0.313\) | A1 [4] |
**(i)**
$6 \times 0.4\cos60 = 0.8 P\cos45$ | M1 | Takes moments about $B$
$P$ is the force at $A$ | A1 |
$P = 2.12\text{N}$ | A1 [3] |
**(ii)**
$F = P\sin75$ (F is friction force at $B$) | B1 | Must use correct angle $(\cos15)$
$R = 6 + P\cos75$ (R is normal reaction at $B$) | B1 | Must use correct angle $(\sin15)$
$\mu = (2.12\sin75)/(6 + 2.12\cos75)$ | M1 |
$\mu = 0.313$ | A1 [4] |2\\
\includegraphics[max width=\textwidth, alt={}, center]{2c6b2e42-09cb-4653-9378-6c6add7771cc-2_463_567_479_790}
A uniform rod $A B$ has weight 6 N and length 0.8 m . The rod rests in limiting equilibrium with $B$ in contact with a rough horizontal surface and $A B$ inclined at $60 ^ { \circ }$ to the horizontal. Equilibrium is maintained by a force, in the vertical plane containing $A B$, acting at $A$ at an angle of $45 ^ { \circ }$ to $A B$ (see diagram). Calculate\\
(i) the magnitude of the force applied at $A$,\\
(ii) the least possible value of the coefficient of friction at $B$.
\hfill \mbox{\textit{CAIE M2 2012 Q2 [7]}}