7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-12_524_586_274_696}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Two particles \(P\) and \(Q\) have masses 3 kg and \(m \mathrm {~kg}\) respectively ( \(m > 3\) ). The particles are connected by a light inextensible string which passes over a smooth light fixed pulley. The system is held at rest with the string taut and the hanging parts of the string vertical. The particle \(Q\) is at a height of 10.5 m above the horizontal ground, as shown in Figure 5. The system is released from rest and \(Q\) moves downwards. In the subsequent motion \(P\) does not reach the pulley. After the system is released, the tension in the string is 33.6 N .
- Show that the magnitude of the acceleration of \(P\) is \(1.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- Find the value of \(m\).
The system is released from rest at time \(t = 0\). At time \(T _ { 1 }\) seconds after release, \(Q\) strikes the ground and does not rebound. The string goes slack and \(P\) continues to move upwards.
- Find the value of \(T _ { 1 }\)
At time \(T _ { 2 }\) seconds after release, \(P\) comes to instantaneous rest.
- Find the value of \(T _ { 2 }\)
At time \(T _ { 3 }\) seconds after release ( \(T _ { 3 } > T _ { 1 }\) ) the string becomes taut again.
- Sketch a velocity-time graph for the motion of \(P\) in the interval \(0 \leqslant t \leqslant T _ { 3 }\)