OCR H240/03 2020 November — Question 10 11 marks

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2020
SessionNovember
Marks11
PaperDownload PDF ↗
TopicMoments
TypeRod hinged to wall with string support
DifficultyStandard +0.3 This is a standard mechanics statics problem requiring moment equilibrium and force resolution. While it involves multiple steps (moments about A, resolving forces, finding resultant), the techniques are routine for A-level mechanics: taking moments about a hinge, resolving in two directions, and using Pythagoras/trigonometry. The geometry is straightforward with given angles and distances. This is slightly easier than average because it's a textbook-style equilibrium problem with clear structure and standard methods, though the multi-part nature and need for careful geometry prevents it from being significantly below average.
Spec3.04b Equilibrium: zero resultant moment and force

\includegraphics{figure_10} The diagram shows a wall-mounted light. It consists of a rod \(AB\) of mass 0.25 kg and length 0.8 m which is freely hinged to a vertical wall at \(A\), and a lamp of mass 0.5 kg fixed at \(B\). The system is held in equilibrium by a chain \(CD\) whose end \(C\) is attached to the midpoint of \(AB\). The end \(D\) is fixed to the wall a distance 0.4 m vertically above \(A\). The rod \(AB\) makes an angle of \(60°\) with the downward vertical. The chain is modelled as a light inextensible string, the rod is modelled as uniform and the lamp is modelled as a particle.
  1. By taking moments about \(A\), determine the tension in the chain. [4]
    1. Determine the magnitude of the force exerted on the rod at \(A\). [4]
    2. Calculate the direction of the force exerted on the rod at \(A\). [2]
  2. Suggest one improvement that could be made to the model to make it more realistic. [1]

\includegraphics{figure_10}

The diagram shows a wall-mounted light. It consists of a rod $AB$ of mass 0.25 kg and length 0.8 m which is freely hinged to a vertical wall at $A$, and a lamp of mass 0.5 kg fixed at $B$. The system is held in equilibrium by a chain $CD$ whose end $C$ is attached to the midpoint of $AB$. The end $D$ is fixed to the wall a distance 0.4 m vertically above $A$. The rod $AB$ makes an angle of $60°$ with the downward vertical.

The chain is modelled as a light inextensible string, the rod is modelled as uniform and the lamp is modelled as a particle.

\begin{enumerate}[label=(\alph*)]
\item By taking moments about $A$, determine the tension in the chain. [4]
\item \begin{enumerate}[label=(\roman*)]
\item Determine the magnitude of the force exerted on the rod at $A$. [4]
\item Calculate the direction of the force exerted on the rod at $A$. [2]
\end{enumerate}
\item Suggest one improvement that could be made to the model to make it more realistic. [1]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/03 2020 Q10 [11]}}