| Exam Board | WJEC |
|---|---|
| Module | Further Unit 6 (Further Unit 6) |
| Year | 2023 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on smooth peg or cylinder |
| Difficulty | Challenging +1.2 This is a standard statics problem requiring resolution of forces and taking moments about a point, with the added feature of limiting equilibrium (F = μR). While it involves multiple steps (resolving horizontally/vertically, taking moments, finding AC), the techniques are routine for Further Maths mechanics. Part (c) requires conceptual understanding but no calculation. Slightly above average due to the multi-part nature and need to handle the geometry carefully, but follows standard textbook methods. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
\begin{enumerate}
\item The diagram shows a uniform rod $A B$, of length 8 m and mass 23 kg , in limiting equilibrium with its end $A$ on rough horizontal ground and point $C$ resting against a smooth fixed cylinder. The rod is inclined at an angle of $30 ^ { \circ }$ to the ground.\\
\includegraphics[max width=\textwidth, alt={}, center]{d7f600c5-af4a-4708-bfd9-92b37a95c634-3_240_869_603_598}
\end{enumerate}
The coefficient of friction between the ground and the rod is $\frac { 2 } { 3 }$.\\
(a) Calculate the magnitude of the normal reaction at $C$ and the magnitude of the normal reaction to the ground at $A$.\\
(b) Find the length $A C$.\\
(c) Suppose instead that the rod is non-uniform with its centre of mass closer to $A$ than to $B$. Without carrying out any further calculations, state whether or not this will affect your answers in part (a). Give a reason for your answer.\\
\hfill \mbox{\textit{WJEC Further Unit 6 2023 Q1 [13]}}