AQA M2 2016 June — Question 4 8 marks

Exam BoardAQA
ModuleM2 (Mechanics 2)
Year2016
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 1
TypeString through hole – hanging particle in equilibrium below table
DifficultyStandard +0.3 This is a standard M2 conical pendulum problem with equilibrium and circular motion. Part (a) is immediate from Q's equilibrium (T=8g). Part (b) requires resolving forces on P vertically and using circular motion horizontally—straightforward application of F=ma and F=mv²/r. Part (c) follows directly from trigonometry. All steps are routine M2 techniques with no novel insight required, making it slightly easier than average.
Spec3.03k Connected particles: pulleys and equilibrium6.05c Horizontal circles: conical pendulum, banked tracks

A particle \(P\), of mass \(6\) kg, is attached to one end of a light inextensible string. The string passes through a small smooth ring, fixed at a point \(O\). A second particle \(Q\), of mass \(8\) kg, is attached to the other end of the string. The particle \(Q\) hangs at rest vertically below the ring, and the particle \(P\) moves with speed \(5 \text{ m s}^{-1}\) in a horizontal circle, as shown in the diagram. The angle between \(OP\) and the vertical is \(\theta\). \includegraphics{figure_4}
  1. Find the tension in the string. [1 mark]
  2. Find \(\theta\). [3 marks]
  3. Find the radius of the horizontal circle. [4 marks]

Question 4:
AnswerMarks
4m
Question 4:
4 | m
A particle $P$, of mass $6$ kg, is attached to one end of a light inextensible string. The string passes through a small smooth ring, fixed at a point $O$. A second particle $Q$, of mass $8$ kg, is attached to the other end of the string.

The particle $Q$ hangs at rest vertically below the ring, and the particle $P$ moves with speed $5 \text{ m s}^{-1}$ in a horizontal circle, as shown in the diagram.

The angle between $OP$ and the vertical is $\theta$.

\includegraphics{figure_4}

\begin{enumerate}[label=(\alph*)]
\item Find the tension in the string.
[1 mark]

\item Find $\theta$.
[3 marks]

\item Find the radius of the horizontal circle.
[4 marks]
\end{enumerate}

\hfill \mbox{\textit{AQA M2 2016 Q4 [8]}}