| 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 +0.8 This is a multi-step statics problem requiring resolution of forces in two directions, taking moments about a point, and applying limiting friction conditions. While the concepts are standard A-level mechanics (equilibrium, moments, friction), the combination of an inclined rod with a force at an angle to the rod (not horizontal/vertical) requires careful geometric reasoning and systematic application of multiple equilibrium conditions across 7 marks. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Takes moments about \(B\) | M1 | |
| \(6 \times 0.4\cos60 = 0.8 P\cos45\) | A1 | |
| \(P = 2.12N\) | A1 [3] | \(P\) is the force at \(A\) |
| 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)
Takes moments about $B$ | M1 |
$6 \times 0.4\cos60 = 0.8 P\cos45$ | A1 |
$P = 2.12N$ | A1 [3] | $P$ is the force at $A$
## (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] |\includegraphics{figure_2}
A uniform rod $AB$ 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 $AB$ inclined at $60°$ to the horizontal. Equilibrium is maintained by a force, in the vertical plane containing $AB$, acting at $A$ at an angle of $45°$ to $AB$ (see diagram). Calculate
\begin{enumerate}[label=(\roman*)]
\item the magnitude of the force applied at $A$, [3]
\item the least possible value of the coefficient of friction at $B$. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2012 Q2 [7]}}