CAIE M1 2009 November — Question 5

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2009
SessionNovember
TopicFriction

5 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{efa7175f-832b-4cd3-82ab-52e402115081-3_317_517_922_468} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{efa7175f-832b-4cd3-82ab-52e402115081-3_317_522_922_1155} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} A small ring of weight 12 N is threaded on a fixed rough horizontal rod. A light string is attached to the ring and the string is pulled with a force of 15 N at an angle of \(30 ^ { \circ }\) to the horizontal.
  1. When the angle of \(30 ^ { \circ }\) is below the horizontal (see Fig. 1), the ring is in limiting equilibrium. Show that the coefficient of friction between the ring and the rod is 0.666 , correct to 3 significant figures.
  2. When the angle of \(30 ^ { \circ }\) is above the horizontal (see Fig. 2), the ring is moving with acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Find the value of \(a\).