5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4fd21e83-0bdf-4bb1-8a3f-76beada511ae-16_359_298_233_824}
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\caption{Figure 3}
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A lift of mass 250 kg is being raised by a vertical cable attached to the top of the lift. A woman of mass 60 kg stands on the horizontal floor inside the lift, as shown in Figure 3. The lift ascends vertically with constant acceleration \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). There is a constant downwards resistance of magnitude 100 N on the lift. By modelling the woman as a particle,
- find the magnitude of the normal reaction exerted by the floor of the lift on the woman.
The tension in the cable must not exceed 10000 N for safety reasons, and the maximum upward acceleration of the lift is \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). A typical occupant of the lift is modelled as a particle of mass 75 kg and the cable is modelled as a light inextensible string. There is still a constant downwards resistance of magnitude 100 N on the lift.
- Find the maximum number of typical occupants that can be safely carried in the lift when it is ascending with an acceleration of \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).