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The diagram shows a plank of wood \(A B\), of mass 10 kg and length 6 m , resting with its end \(A\) on rough horizontal ground and its end \(B\) in contact with a fixed cylindrical oil drum. The plank is in a vertical plane perpendicular to the axis of the drum, and the line \(A B\) is a tangent to the circular cross-section of the drum, with the point of contact at \(B\). The plank is inclined at an angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 5 } { 12 }\).
The plank is modelled as a uniform rod and the oil drum is modelled as being smooth.
- Find, in terms of \(g\), the normal contact force between the drum and the plank.
- Given that the plank is in limiting equilibrium, find the coefficient of friction between the plank and the ground.