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A beam, \(A B\), has length 4 m and mass 20 kg . The beam is suspended horizontally by two vertical ropes. One rope is attached to the beam at \(C\), where \(A C = 0.5 \mathrm {~m}\). The other rope is attached to the beam at \(D\), where \(D B = 0.7 \mathrm {~m}\) (see diagram).
The beam is modelled as a non-uniform rod and the ropes as light inextensible strings.
It is given that the tension in the rope at \(C\) is three times the tension in the rope at \(D\).
- Determine the distance of the centre of mass of the beam from \(A\).
A particle of mass \(m \mathrm {~kg}\) is now placed on the beam at a point where the magnitude of the moment of the particle's weight about \(C\) is 3.5 mg N m . The beam remains horizontal and in equilibrium.
- Determine the largest possible value of \(m\).