8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ca445c1e-078c-4a57-94df-de90f30f8efd-20_369_1264_248_342}
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\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.
- 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,
- find, in terms of \(h\), the range of possible values of \(d\).
- State one physical factor, other than air resistance, that could be taken into account to make the model described above more realistic.