5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7ba14d10-1b57-4930-8d65-f21088c5d513-08_315_817_255_587}
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\caption{Figure 2}
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A beam \(A B\) has mass 12 kg and length 5 m . It is held in equilibrium in a horizontal position by two vertical ropes attached to the beam. One rope is attached to \(A\), the other to the point \(C\) on the beam, where \(B C = 1 \mathrm {~m}\), as shown in Figure 2. The beam is modelled as a uniform rod, and the ropes as light strings.
- Find
- the tension in the rope at \(C\),
- the tension in the rope at \(A\).
A small load of mass 16 kg is attached to the beam at a point which is \(y\) metres from \(A\). The load is modelled as a particle. Given that the beam remains in equilibrium in a horizontal position,
- find, in terms of \(y\), an expression for the tension in the rope at \(C\).
The rope at \(C\) will break if its tension exceeds 98 N. The rope at \(A\) cannot break.
- Find the range of possible positions on the beam where the load can be attached without the rope at \(C\) breaking.