7.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{57a51cfd-7206-4f34-9744-44255789188d-5_196_1100_363_506}
\end{figure}
Two particles \(P\) and \(Q\), of mass 4 kg and 6 kg respectively, are joined by a light inextensible string. Initially the particles are at rest on a rough horizontal plane with the string taut. The coefficient of friction between each particle and the plane is \(\frac { 2 } { 7 }\). A constant force of magnitude 40 N is then applied to \(Q\) in the direction \(P Q\), as shown in Fig. 4.
- Show that the acceleration of \(Q\) is \(1.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- Calculate the tension in the string when the system is moving.
- State how you have used the information that the string is inextensible.
After the particles have been moving for 7 s , the string breaks. The particle \(Q\) remains under the action of the force of magnitude 40 N .
- Show that \(P\) continues to move for a further 3 seconds.
- Calculate the speed of \(Q\) at the instant when \(P\) comes to rest.
END