OCR M3 2010 June — Question 2 7 marks

Exam BoardOCR
ModuleM3 (Mechanics 3)
Year2010
SessionJune
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeRod or block on rough surface in limiting equilibrium (no wall)
DifficultyStandard +0.3 This is a standard two-rod statics problem requiring moment equilibrium and force resolution. The geometry is straightforward (vertical alignment given), and the method is routine: take moments about A, then resolve forces. While it requires careful bookkeeping of forces and multiple steps, it follows a standard M3 template with no novel insight needed—slightly easier than average A-level.
Spec3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces

\includegraphics{figure_2} Two uniform rods \(AB\) and \(BC\) are of equal length and each has weight \(100\) N. The rods are freely jointed to each other at \(B\), and \(A\) is freely jointed to a fixed point. The rods are in equilibrium in a vertical plane with \(AB\) horizontal and \(C\) resting on a rough horizontal surface. \(C\) is vertically below the mid-point of \(AB\) (see diagram).
  1. By taking moments about \(A\) for \(AB\), find the vertical component of the force on \(AB\) at \(B\). Hence find the vertical component of the contact force on \(BC\) at \(C\). [3]
  2. Calculate the magnitude of the frictional force on \(BC\) at \(C\) and state its direction. [4]

\includegraphics{figure_2}

Two uniform rods $AB$ and $BC$ are of equal length and each has weight $100$ N. The rods are freely jointed to each other at $B$, and $A$ is freely jointed to a fixed point. The rods are in equilibrium in a vertical plane with $AB$ horizontal and $C$ resting on a rough horizontal surface. $C$ is vertically below the mid-point of $AB$ (see diagram).

\begin{enumerate}[label=(\roman*)]
\item By taking moments about $A$ for $AB$, find the vertical component of the force on $AB$ at $B$. Hence find the vertical component of the contact force on $BC$ at $C$. [3]
\item Calculate the magnitude of the frictional force on $BC$ at $C$ and state its direction. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR M3 2010 Q2 [7]}}