7.
\begin{figure}[h]
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\caption{Figure 3}
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\end{figure}
Particles \(A\) and \(B\), of mass \(2 m\) and \(m\) respectively, are attached to the ends of a light inextensible string. The string passes over a small smooth pulley fixed at the edge of a rough horizontal table. Particle \(A\) is held on the table, while \(B\) rests on a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal, as shown in Fig. 3. The string is in the same vertical plane as a line of greatest slope of the inclined plane. The coefficient of friction between \(A\) and the table is \(\mu\). The particle \(A\) is released from rest and begins to move.
By writing down an equation of motion for each particle,
- show that, while both particles move with the string taut. Each particle has an acceleration of magnitude \(\frac { 1 } { 6 } ( 1 - 4 \mu ) g\).
When each particle has moved a distance \(h\), the string breaks. The particle \(A\) comes to rest before reaching the pulley. Given that \(\mu = 0.2\),
- find, in terms of \(h\), the total distance moved by \(A\).
For the model described above,
- state two physical factors, apart from air resistance, which could be taken into account to make the model more realistic.