Edexcel M1 2023 October — Question 5

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2023
SessionOctober
TopicFriction

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{017cc2b0-9ec3-45ff-94c0-9d989badfd5d-16_757_460_246_804} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A small ring of mass 0.2 kg is attached to one end of a light inextensible string.
The ring is threaded onto a fixed rough vertical rod.
The string is taut and makes an angle \(\theta\) with the rod, as shown in Figure 3, where \(\tan \theta = \frac { 12 } { 5 }\) Given that the ring is in equilibrium and that the tension in the string is 10 N ,
  1. find the magnitude of the frictional force acting on the ring,
  2. state the direction of the frictional force acting on the ring. The coefficient of friction between the ring and the rod is \(\frac { 1 } { 4 }\)
    Given that the ring is in equilibrium, and that the tension in the string, \(T\) newtons, can now vary,
    1. find the minimum value of \(T\)
    2. find the maximum value of \(T\)