WJEC Further Unit 6 2023 June — Question 1 13 marks

Exam BoardWJEC
ModuleFurther Unit 6 (Further Unit 6)
Year2023
SessionJune
Marks13
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeRod on smooth peg or cylinder
DifficultyChallenging +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.
Spec3.03t 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

  1. 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}
The coefficient of friction between the ground and the rod is \(\frac { 2 } { 3 }\).
  1. Calculate the magnitude of the normal reaction at \(C\) and the magnitude of the normal reaction to the ground at \(A\).
  2. Find the length \(A C\).
  3. 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.

\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]}}