3.
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\caption{Figure 1}
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\end{figure}
A seesaw in a playground consists of a beam \(A B\) of length 4 m which is supported by a smooth pivot at its centre \(C\). Jill has mass 25 kg and sits on the end \(A\). David has mass 40 kg and sits at a distance \(x\) metres from \(C\), as shown in Figure 1. The beam is initially modelled as a uniform rod. Using this model,
- find the value of \(x\) for which the seesaw can rest in equilibrium in a horizontal position.
- State what is implied by the modelling assumption that the beam is uniform.
David realises that the beam is not uniform as he finds that he must sit at a distance 1.4 m from \(C\) for the seesaw to rest horizontally in equilibrium. The beam is now modelled as a non-uniform rod of mass 15 kg . Using this model,
- find the distance of the centre of mass of the beam from \(C\).