OCR M2 — Question 3 8 marks

Exam BoardOCR
ModuleM2 (Mechanics 2)
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 1
TypeSmooth ring on rotating string
DifficultyStandard +0.3 This is a standard conical pendulum problem requiring resolution of forces and circular motion equations. The geometry is given, making it straightforward to find angles and apply T cos θ = mg and T sin θ = mω²r. While it involves multiple steps across three parts, each follows routine M2 procedures without requiring novel insight or complex problem-solving.
Spec6.02e Calculate KE and PE: using formulae6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks

\includegraphics{figure_3} One end of a light inextensible string of length 1.6 m is attached to a point \(P\). The other end is attached to the point \(Q\), vertically below \(P\), where \(PQ = 0.8\) m. A small smooth bead \(B\), of mass 0.01 kg, is threaded on the string and moves in a horizontal circle, with centre \(Q\) and radius 0.6 m. \(QB\) rotates with constant angular speed \(\omega\) rad s\(^{-1}\) (see diagram).
  1. Show that the tension in the string is 0.1225 N. [3]
  2. Find \(\omega\). [3]
  3. Calculate the kinetic energy of the bead. [2]

\includegraphics{figure_3}

One end of a light inextensible string of length 1.6 m is attached to a point $P$. The other end is attached to the point $Q$, vertically below $P$, where $PQ = 0.8$ m. A small smooth bead $B$, of mass 0.01 kg, is threaded on the string and moves in a horizontal circle, with centre $Q$ and radius 0.6 m. $QB$ rotates with constant angular speed $\omega$ rad s$^{-1}$ (see diagram).

\begin{enumerate}[label=(\roman*)]
\item Show that the tension in the string is 0.1225 N. [3]
\item Find $\omega$. [3]
\item Calculate the kinetic energy of the bead. [2]
\end{enumerate}

\hfill \mbox{\textit{OCR M2  Q3 [8]}}