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A barrier is modelled as a uniform rectangular plank of wood, \(A B C D\), rigidly joined to a uniform square metal plate, \(D E F G\). The plank of wood has mass 50 kg and dimensions 4.0 m by 0.25 m . The metal plate has mass 80 kg and side 0.5 m . The plank and plate are joined in such a way that \(C D E\) is a straight line (see diagram). The barrier is smoothly pivoted at the point \(D\). In the closed position, the barrier rests on a thin post at \(H\). The distance \(C H\) is 0.25 m .
- Calculate the contact force at \(H\) when the barrier is in the closed position.
In the open position, the centre of mass of the barrier is vertically above \(D\).
- Calculate the angle between \(A B\) and the horizontal when the barrier is in the open position.