OCR MEI M1 2016 June — Question 3

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2016
SessionJune
TopicPulley systems

3 Fig. 3.1 shows a block of mass 8 kg on a smooth horizontal table.
This block is connected by a light string passing over a smooth pulley to a block of mass 4 kg which hangs freely. The part of the string between the 8 kg block and the pulley is parallel to the table. The system has acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c8c96cf-5184-46e4-9c45-a8a80d0a6ff8-3_330_809_525_628} \captionsetup{labelformat=empty} \caption{Fig. 3.1}
\end{figure}
  1. Write down two equations of motion, one for each block.
  2. Find the value of \(a\). The table is now tilted at an angle of \(\theta\) to the horizontal as shown in Fig. 3.2. The system is set up as before; the 4 kg block still hangs freely. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{4c8c96cf-5184-46e4-9c45-a8a80d0a6ff8-3_410_727_1324_669} \captionsetup{labelformat=empty} \caption{Fig. 3.2}
    \end{figure}
  3. The system is now in equilibrium. Find the value of \(\theta\).