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}
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\caption{Fig. 1.1}
\end{figure}
- Calculate the acceleration of the cylinder when the tension in the wire is 1000 N .
- 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}
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\caption{Fig. 1.2}
\end{figure} - Calculate the new tension in the wire.