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\(A B C D\) is the cross-section through the centre of mass of a uniform rectangular block of weight 260 N . The lengths \(A B\) and \(B C\) are 1.5 m and 0.8 m respectively. The block rests in equilibrium with the point \(D\) on a rough horizontal floor. Equilibrium is maintained by a light rope attached to the point \(A\) on the block and the point \(E\) on the floor. The points \(E , A\) and \(B\) lie in a straight line inclined at \(30 ^ { \circ }\) to the horizontal (see diagram).
- By taking moments about \(D\), show that the tension in the rope is 146 N , correct to 3 significant figures.
- Given that the block is in limiting equilibrium, calculate the coefficient of friction between the block and the floor.