3.
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\caption{Fig. 1}
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Figure 1 shows a ladder of mass 20 kg and length 6 m leaning against a rough vertical wall with its lower end on smooth horizontal ground. The ladder is prevented from slipping along the ground by a light rope which is attached to the ladder 2 m from its bottom end and fastened to the wall so that the rope is horizontal and perpendicular to the wall.
The ladder is at an angle \(\theta\) to the horizontal where \(\tan \theta = \frac { 5 } { 2 }\) and the coefficient of friction between the ladder and the wall is \(\frac { 1 } { 3 }\).
- Draw a diagram showing all the forces acting on the ladder.
- Show that the magnitude of the tension in the rope is \(5 g\).
A man wishes to use the ladder but fears the rope will snap as he climbs the ladder.
- Suggest, giving a reason for your answer, a more suitable position for the rope.
(2 marks)