M1 January 2013 Q2

EdexcelOld spec9 marksMoments

2. A steel girder \(AB\), of mass 200 kg and length 12 m, rests horizontally in equilibrium on two smooth supports at \(C\) and at \(D\), where \(AC = 2\) m and \(DB = 2\) m. A man of mass 80 kg stands on the girder at the point \(P\), where \(AP = 4\) m, as shown in Figure 1.

Figure 1: girder AB of length 12 m on supports at C and D, AC = 2 m, DB = 2 m, man at P with AP = 4 m
Figure 1

The man is modelled as a particle and the girder is modelled as a uniform rod.

(a) Find the magnitude of the reaction on the girder at the support at \(C\). (3)

The support at \(D\) is now moved to the point \(X\) on the girder, where \(XB = x\) metres. The man remains on the girder at \(P\), as shown in Figure 2.

Figure 2: girder AB of length 12 m on supports at C and X, AC = 2 m, XB = x m, man at P with AP = 4 m
Figure 2

Given that the magnitudes of the reactions at the two supports are now equal and that the girder again rests horizontally in equilibrium, find

(b) the magnitude of the reaction at the support at \(X\), (2)
(c) the value of \(x\). (4)
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