OCR MEI M1 2008 June — Question 1

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2008
SessionJune
TopicNewton's laws and connected particles

1 Fig. 1.1 shows a circular cylinder of mass 100 kg being raised by a light, inextensible vertical wire AB . There is negligible air resistance. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{170edb27-324e-44df-8dc1-7d8fbad680fe-2_310_261_488_941} \captionsetup{labelformat=empty} \caption{Fig. 1.1}
\end{figure}
  1. Calculate the acceleration of the cylinder when the tension in the wire is 1000 N .
  2. Calculate the tension in the wire when the cylinder has an upward acceleration of \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The cylinder is now raised inside a fixed smooth vertical tube that prevents horizontal motion but provides negligible resistance to the upward motion of the cylinder. When the wire is inclined at \(30 ^ { \circ }\) to the vertical, as shown in Fig. 1.2, the cylinder again has an upward acceleration of \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{170edb27-324e-44df-8dc1-7d8fbad680fe-2_305_490_1354_829} \captionsetup{labelformat=empty} \caption{Fig. 1.2}
    \end{figure}
  3. Calculate the new tension in the wire.