3.
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\caption{Figure 2}
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A beam \(A D C B\) has length 5 m . The beam lies on a horizontal step with the end \(A\) on the step and the end \(B\) projecting over the edge of the step. The edge of the step is at the point \(D\) where \(D B = 1.3 \mathrm {~m}\), as shown in Figure 2.
When a small boy of mass 30 kg stands on the beam at \(C\), where \(C B = 0.5 \mathrm {~m}\), the beam is on the point of tilting.
The boy is modelled as a particle and the beam is modelled as a uniform rod.
- Find the mass of the beam.
A block of mass \(X \mathrm {~kg}\) is now placed on the beam at \(A\).
The block is modelled as a particle. - Find the smallest value of \(X\) that will enable the boy to stand on the beam at \(B\) without the beam tilting.
- State how you have used the modelling assumption that the block is a particle in your calculations.