CAIE M2 2016 June — Question 6 9 marks

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2016
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 1
TypeSmooth ring on rotating string
DifficultyStandard +0.3 This is a standard circular motion problem requiring resolution of forces and application of F=mrω². The geometry is straightforward (3-4-5 triangle), and the two parts follow predictable patterns: (i) finding angular speed from given tension, (ii) finding speed at limiting case when normal reaction becomes zero. Slightly above average due to 3D geometry and two-part structure, but uses routine A-level mechanics techniques without requiring novel insight.
Spec6.05c Horizontal circles: conical pendulum, banked tracks

\includegraphics{figure_6} A light inextensible string passes through a small smooth bead \(B\) of mass \(0.4 \text{ kg}\). One end of the string is attached to a fixed point \(A\) \(0.4 \text{ m}\) above a fixed point \(O\) on a smooth horizontal surface. The other end of the string is attached to a fixed point \(C\) which is vertically below \(A\) and \(0.3 \text{ m}\) above the surface. The bead moves with constant speed on the surface in a circle with centre \(O\) and radius \(0.3 \text{ m}\) (see diagram).
  1. Given that the tension in the string is \(2 \text{ N}\), calculate
    1. the angular speed of the bead, [3]
    2. the magnitude of the contact force exerted on the bead by the surface. [2]
  2. Given instead that the bead is about to lose contact with the surface, calculate the speed of the bead. [4]

\includegraphics{figure_6}

A light inextensible string passes through a small smooth bead $B$ of mass $0.4 \text{ kg}$. One end of the string is attached to a fixed point $A$ $0.4 \text{ m}$ above a fixed point $O$ on a smooth horizontal surface. The other end of the string is attached to a fixed point $C$ which is vertically below $A$ and $0.3 \text{ m}$ above the surface. The bead moves with constant speed on the surface in a circle with centre $O$ and radius $0.3 \text{ m}$ (see diagram).

\begin{enumerate}[label=(\roman*)]
\item Given that the tension in the string is $2 \text{ N}$, calculate
\begin{enumerate}[label=(\alph*)]
\item the angular speed of the bead, [3]
\item the magnitude of the contact force exerted on the bead by the surface. [2]
\end{enumerate}
\item Given instead that the bead is about to lose contact with the surface, calculate the speed of the bead. [4]
\end{enumerate}

\hfill \mbox{\textit{CAIE M2 2016 Q6 [9]}}