Edexcel M1 2021 January — Question 8

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2021
SessionJanuary
TopicPulley systems

8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ca445c1e-078c-4a57-94df-de90f30f8efd-20_369_1264_248_342} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Two particles, \(A\) and \(B\), have masses 2 kg and 4 kg respectively. The particles are connected by a light inextensible string. The string passes over a small smooth pulley which is fixed at the top of a rough plane. The plane is inclined to the horizontal ground at an angle \(\alpha\) where \(\tan \alpha = \frac { 3 } { 4 }\). The particle \(A\) is held at rest on the plane at a distance \(d\) metres from the pulley. The particle \(B\) hangs freely at rest, vertically below the pulley, at a distance \(h\) metres above the ground, as shown in Figure 3. The part of the string between \(A\) and the pulley is parallel to a line of greatest slope of the plane. The coefficient of friction between \(A\) and the plane is \(\frac { 1 } { 4 }\) The system is released from rest with the string taut and \(B\) descends.
  1. Find the tension in the string as \(B\) descends. On hitting the ground, \(B\) immediately comes to rest. Given that \(A\) comes to rest before reaching the pulley,
  2. find, in terms of \(h\), the range of possible values of \(d\).
  3. State one physical factor, other than air resistance, that could be taken into account to make the model described above more realistic.