Edexcel M1 2020 January — Question 4

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2020
SessionJanuary
TopicFriction

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{916543cb-14f7-486c-ba3c-eda9be134045-10_633_1237_258_356} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Two identical small rings, \(A\) and \(B\), each of mass \(m\), are threaded onto a rough horizontal wire. The rings are connected by a light inextensible string. A particle \(C\) of mass \(3 m\) is attached to the midpoint of the string. The particle \(C\) hangs in equilibrium below the wire with angle \(B A C = \beta\), as shown in Figure 2. The tension in each of the parts, \(A C\) and \(B C\), of the string is \(T\)
  1. By considering particle \(C\), find \(T\) in terms of \(m , g\) and \(\beta\)
  2. Find, in terms of \(m\) and \(g\), the magnitude of the normal reaction between the wire and \(A\). The coefficient of friction between each ring and the wire is \(\frac { 4 } { 5 }\)
    The two rings, \(A\) and \(B\), are on the point of sliding along the wire towards each other.
  3. Find the value of \(\tan \beta\)
    \includegraphics[max width=\textwidth, alt={}, center]{916543cb-14f7-486c-ba3c-eda9be134045-11_2255_50_314_34}
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