AQA M2 2012 January — Question 7 11 marks

Exam BoardAQA
ModuleM2 (Mechanics 2)
Year2012
SessionJanuary
Marks11
PaperDownload PDF ↗
TopicCircular Motion 1
TypeVertical circle – string/rod (tension and energy)
DifficultyStandard +0.3 This is a standard M2 vertical circular motion problem requiring energy conservation and Newton's second law at two positions. Part (a) is a straightforward 'show that' using energy methods, while part (b) involves setting up tension equations at two points and solving simultaneous equations. The multi-step nature and need to combine energy and force equations makes it slightly above average, but it follows a well-practiced template for this topic with no novel insight required.
Spec6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods

  1. Show that \(v ^ { 2 } = u ^ { 2 } - 4 a g\).
  2. The ratio of the tensions in the string when the bead is at the two points \(A\) and \(B\) is \(2 : 5\).
    1. Find \(u\) in terms of \(g\) and \(a\).
    2. Find the ratio \(u : v\).

\begin{enumerate}[label=(\alph*)]
\item Show that $v ^ { 2 } = u ^ { 2 } - 4 a g$.
\item The ratio of the tensions in the string when the bead is at the two points $A$ and $B$ is $2 : 5$.
\begin{enumerate}[label=(\roman*)]
\item Find $u$ in terms of $g$ and $a$.
\item Find the ratio $u : v$.
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA M2 2012 Q7 [11]}}