3 The diagram shows a uniform beam AB , of weight 80 N and length 7 m , resting in equilibrium in a vertical plane. The end A is in contact with a rough vertical wall, and the angle between the beam and the upward vertical is \(60 ^ { \circ }\). The beam is supported by a smooth peg at a point C , where \(\mathrm { AC } = 2 \mathrm {~m}\).
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1. Complete the diagram in the Printed Answer Booklet to show all the forces acting on the beam.
2. 1. Show that the magnitude of the frictional force exerted on the beam by the wall is 25 N .
   2. Hence determine the magnitude of the total contact force exerted on the beam by the wall.
3. Determine the direction of the total contact force exerted on the beam by the wall. The coefficient of friction between the beam and the wall is \(\mu\).
4. Find the range of possible values for \(\mu\).
5. Explain how your answer to part (b)(ii) would change if the peg were situated closer to A but the angle between the beam and the upward vertical remained at \(60 ^ { \circ }\).