M1 June 2018 Q3

EdexcelOld spec7 marksMoments

3.

Figure 2: horizontal beam AB of length 9 m held by vertical ropes at C and D, with AC = 1.5 m, BD = 3.5 m and a gymnast at P where AP = 3 m
Figure 2

A wooden beam \(AB\), of mass 150 kg and length 9 m, rests in a horizontal position supported by two vertical ropes. The ropes are attached to the beam at \(C\) and \(D\), where \(AC = 1.5\) m and \(BD = 3.5\) m. A gymnast of mass 60 kg stands on the beam at the point \(P\), where \(AP = 3\) m, as shown in Figure 2. The beam remains horizontal and in equilibrium.

By modelling the gymnast as a particle, the beam as a uniform rod and the ropes as light inextensible strings,

(a) find the tension in the rope attached to the beam at \(C\). (3)

The gymnast at \(P\) remains on the beam at \(P\) and another gymnast, who is also modelled as a particle, stands on the beam at \(B\). The beam remains horizontal and in equilibrium. The mass of the gymnast at \(B\) is the largest possible for which the beam remains horizontal and in equilibrium.

(b) Find the tension in the rope attached to the beam at \(D\). (4)
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