A non-uniform beam $$\(A B\)$$ has length $$\(6 \mathrm{~m}\)$$ and weight $$\(W\)$$ newtons. The beam is supported in equilibrium in a horizontal position by two vertical ropes, one attached to the beam at $$\(A\)$$ and the other attached to the beam at $$\(C\)$$, where $$\(C B=1.5 \mathrm{~m}\)$$, as shown in Figure 1. The centre of mass of the beam is $$\(2.625 \mathrm{~m}\)$$ from $$\(A\)$$. The ropes are modelled as light strings. The beam is modelled as a non-uniform rod. Given that the tension in the rope attached at $$\(C\)$$ is $$\(20 \mathrm{~N}\)$$ greater than the tension in the rope attached at $$\(A\)$$, (a) find the value of $$\(W\)$$. (6) (b) State how you have used the fact that the beam is modelled as a rod. (1)

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