4.
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\caption{Figure 2}
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\end{figure}
A uniform plank \(A B\) has weight 80 N and length \(x\) metres. The plank rests in equilibrium horizontally on two smooth supports at \(A\) and \(C\), where \(A C = 2 \mathrm {~m}\), as shown in Fig. 2. A rock of weight 20 N is placed at \(B\) and the plank remains in equilibrium. The reaction on the plank at \(C\) has magnitude 90 N . The plank is modelled as a rod and the rock as a particle.
- Find the value of \(x\).
- State how you have used the model of the rock as a particle.
The support at \(A\) is now moved to a point \(D\) on the plank and the plank remains in equilibrium with the rock at \(B\). The reaction on the plank at \(C\) is now three times the reaction at \(D\).
- Find the distance \(A D\).