7 Fig. 7.1 shows one end of a light inextensible string attached to a block A of mass 4.4 kg . The other end of the string is attached to a block B of mass 5.2 kg .
Block A is in contact with a smooth horizontal plane. The string is taut and passes over a small smooth pulley at the end of the plane. Block B is inside a hollow vertical tube and the vertical sides of B are in contact with the tube. Initially B is 1.6 m above the horizontal base of the tube.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b20e2254-955e-466c-8161-9614d8ccdba0-7_641_771_559_264}
\captionsetup{labelformat=empty}
\caption{Fig. 7.1}
\end{figure}
The blocks are released from rest. It may be assumed that in the subsequent motion A does not reach the pulley and the string remains taut.
Block B reaches the base of the tube with speed \(3.5 \mathrm {~ms} ^ { - 1 }\).
- Given that the frictional force exerted by the tube on B is constant, use an energy method to show that the magnitude of this force is 14.21 N .
Blocks A and B remain attached to the opposite ends of a light inextensible string, but A is now in contact with a rough plane inclined at \(\theta ^ { \circ }\) to the horizontal, as shown in Fig. 7.2.
The string connecting A and B is taut and passes over a small smooth pulley at the top of the plane. Block B is inside the same hollow vertical tube as before with the vertical sides of B in contact with the tube. It may be assumed that the frictional force exerted by the tube on B remains unchanged.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b20e2254-955e-466c-8161-9614d8ccdba0-8_623_723_552_260}
\captionsetup{labelformat=empty}
\caption{Fig. 7.2}
\end{figure}
The coefficient of friction between block A and the plane is \(\frac { 3 } { 11 }\).
The blocks are released from rest, with block B 1.6 m above the base of the tube. It may be assumed that in the subsequent motion A does not reach the pulley and the string remains taut. - Given that block B reaches the base of the tube with speed \(0.7 \mathrm {~ms} ^ { - 1 }\), show that \(\theta\) satisfies the equation
\(3 \cos \theta + 11 \sin \theta = k\),
where \(k\) is a constant to be determined.
\section*{END OF QUESTION PAPER}
\section*{}