| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with rough contact at free end |
| Difficulty | Standard +0.3 This is a straightforward 2D statics problem requiring moments about a point and resolution of forces. The setup is simple (rod perpendicular to wall, single string), and the methods are standard M2 techniques: take moments about A to find T, then resolve forces to find friction coefficient. Slightly easier than average due to the perpendicular orientation simplifying calculations. |
| 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 |
|---|---|---|
| (i) \(9 \times 0.4 = 0.6 \times T\sin30\) | M1 | Moments about A |
| \(T = 12N\) | A1 | [2] |
| (ii) \(\mu = (9 - 12\sin30)/(12\cos30)\) | M1 | For resolving horizontally and vertically |
| \(\mu = (9 - 12\sin30)/(12\cos30)\) | M1 | For using \(F = \mu R\) |
| \(\mu = 0.289\) | A1 | [3] |
**(i)** $9 \times 0.4 = 0.6 \times T\sin30$ | M1 | Moments about A
$T = 12N$ | A1 | [2]
**(ii)** $\mu = (9 - 12\sin30)/(12\cos30)$ | M1 | For resolving horizontally and vertically
$\mu = (9 - 12\sin30)/(12\cos30)$ | M1 | For using $F = \mu R$
$\mu = 0.289$ | A1 | [3]\includegraphics{figure_1}
A non-uniform rod $AB$, of length 0.6 m and weight 9 N, has its centre of mass 0.4 m from $A$. The end $A$ of the rod is in contact with a rough vertical wall. The rod is held in equilibrium, perpendicular to the wall, by means of a light string attached to $B$. The string is inclined at $30°$ to the horizontal. The tension in the string is $T$ N (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Calculate $T$. [2]
\item Find the least possible value of the coefficient of friction at $A$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2011 Q1 [5]}}